The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and ...The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an im...An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced.展开更多
The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions (BCs) axe analyzed, i.e., a constant (Case 1) and a linear streamwise va...The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions (BCs) axe analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanopaxticle volume fraction and wall temperature (Case 2). The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The...The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio...This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.展开更多
In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary...In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.展开更多
An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the ex...An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.展开更多
A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-ele...A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.展开更多
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional...For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.展开更多
The numerical solution of dam toe line is solved based on the dam data and topographic map of dam located. The display of dam perspective is also realized by programming of using VC++ and OpenGL. The research results ...The numerical solution of dam toe line is solved based on the dam data and topographic map of dam located. The display of dam perspective is also realized by programming of using VC++ and OpenGL. The research results above provide the foundation of construction design, construction lofting and information inquiry, which avoids the drawbacks of only using blueprints to do the same work in the past. The method used is useful in practical engineering.展开更多
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian ...In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method.展开更多
In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt+auxx + bu + cu^p+ du^2p-1=0, which contain...In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt+auxx + bu + cu^p+ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions: numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.展开更多
A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the unif...A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.展开更多
In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by deter...In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (Gl/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.展开更多
A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational ma...A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.展开更多
Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general app...Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.展开更多
In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of r...In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions: numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.展开更多
Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. ...Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.展开更多
文摘The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced.
文摘The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions (BCs) axe analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanopaxticle volume fraction and wall temperature (Case 2). The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
文摘The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.
文摘In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.
基金National Natural Science Foundation of China(No.11371087)
文摘An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.
基金Supported by Chinese National Programs for High Technology Research and Development(2008AA042207)
文摘A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair.
基金the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
文摘For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
基金Supported by the Science and Technology Research Key Project of Educational Ministry(01054)
文摘The numerical solution of dam toe line is solved based on the dam data and topographic map of dam located. The display of dam perspective is also realized by programming of using VC++ and OpenGL. The research results above provide the foundation of construction design, construction lofting and information inquiry, which avoids the drawbacks of only using blueprints to do the same work in the past. The method used is useful in practical engineering.
基金The project supported by National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412+2 种基金Natural Science Foundation of Zhejiang Province under Grant No.Y604056Doctoral Science Foundation of Ningbo City under Grant No.2005A61030Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0734
文摘In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method.
基金supported by National Natural Science Foundation of China under Grant No.10735030Natural Science Foundation of Zhejiang Province of China under Grant No.Y604056Doctoral Science Foundation of Ningbo City under Grant No.2005A61030
文摘In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt+auxx + bu + cu^p+ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions: numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.
文摘A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.
文摘In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (Gl/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.
基金supported by the Natural Science Foundation of Hebei Province under Grant No.A2012203407
文摘A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.
文摘Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.
基金National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412+2 种基金Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A61030K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions: numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.
基金National Natural Science Foundation of China under contract No.59839330by ChinaPostdoctoral Science Foundation.
文摘Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.