In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is...In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.展开更多
In this paper,the approximate expressions of the solitary wave solutions for a class of nonlinear disturbedlong-wave system are constructed using the homotopic mapping method.
This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation and a coupled modified Korteweg-de Vries (mKdV)...This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation and a coupled modified Korteweg-de Vries (mKdV) equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.展开更多
The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose...The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.展开更多
In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of...In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.展开更多
In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in term...In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;(F,β) where E;(F,β) is the error in approximating of the function F(s) by definite integral polynomials in the half plane Res≤β<α.展开更多
A method of solving an ultracold trapped ion at the node of the standing wave laser without rotating wave approximation is proposed and the analytical forms of the eigenfunctions and eigenenergies of the system are pr...A method of solving an ultracold trapped ion at the node of the standing wave laser without rotating wave approximation is proposed and the analytical forms of the eigenfunctions and eigenenergies of the system are presented.展开更多
A anified plasma sheath model and its potential equation are proposed. Any higher-ordor-approximation analytical solutions for the unified plasma sheath potential equa tiop are derived by double decomposition method.
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution...An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.展开更多
This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifuga...This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.展开更多
In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-simi...In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.展开更多
We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris ...We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.展开更多
In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approxima...In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.展开更多
In this paper,the approximate analytical oscillatory solutions to the generalized KolmogorovPetrovsky-Piskunov equation(gKPPE for short)are discussed by employing the theory of dynamical system and hypothesis undeterm...In this paper,the approximate analytical oscillatory solutions to the generalized KolmogorovPetrovsky-Piskunov equation(gKPPE for short)are discussed by employing the theory of dynamical system and hypothesis undetermined method.According to the corresponding dynamical system of the bounded traveling wave solutions to the gKPPE,the number and qualitative properties of these bounded solutions are received.Furthermore,pulses(bell-shaped)and waves fronts(kink-shaped)of the gKPPE are given.In particular,two types of approximate analytical oscillatory solutions are constructed.Besides,the error estimations between the approximate analytical oscillatory solutions and the exact solutions of the gKPPE are obtained by the homogeneity principle.Finally,the approximate analytical oscillatory solutions are compared with the numerical solutions,which shows the two types of solutions are similar.展开更多
We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime.Using the minimal geometric deformation(MGD)approach,we split the highly nonlinear coupled field equations into two...We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime.Using the minimal geometric deformation(MGD)approach,we split the highly nonlinear coupled field equations into two subsystems that describe the background geometry and scalar field source,respectively.By considering the Schwarzschild-AdS metric as background geometry,we derive analytical approximate solutions of the scalar field and deformation metric functions using the homotopy analysis method(HAM),providing their analytical approximations to fourth order.Moreover,we discuss the accuracy of the analytical approximations,showing they are sufficiently accurate throughout the exterior spacetime.展开更多
基金supported in part by the National Key Research and Development Program(2021YFF1500100)Key Basic Research of Basic Strengthening Program of the Science and Technology Commission(2020-JCJQ-ZD-068)。
文摘In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper,the approximate expressions of the solitary wave solutions for a class of nonlinear disturbedlong-wave system are constructed using the homotopic mapping method.
基金*Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation and a coupled modified Korteweg-de Vries (mKdV) equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.
文摘The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.
文摘In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.
文摘In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;(F,β) where E;(F,β) is the error in approximating of the function F(s) by definite integral polynomials in the half plane Res≤β<α.
文摘A method of solving an ultracold trapped ion at the node of the standing wave laser without rotating wave approximation is proposed and the analytical forms of the eigenfunctions and eigenenergies of the system are presented.
文摘A anified plasma sheath model and its potential equation are proposed. Any higher-ordor-approximation analytical solutions for the unified plasma sheath potential equa tiop are derived by double decomposition method.
基金This work was financially supported by the National Natural Science Foundation of China (No.50476083).
文摘An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
文摘This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
文摘In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.
基金Project supported by the Fund from the Science and Technology Committee of Shanghai Municipality,China (Grant No. 11ZR1412300)the National Natural Science Foundation of China (Grant No. 61108010)
文摘We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.
文摘In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
基金supported by the National Natural Science Foundation of China (No.11471215)。
文摘In this paper,the approximate analytical oscillatory solutions to the generalized KolmogorovPetrovsky-Piskunov equation(gKPPE for short)are discussed by employing the theory of dynamical system and hypothesis undetermined method.According to the corresponding dynamical system of the bounded traveling wave solutions to the gKPPE,the number and qualitative properties of these bounded solutions are received.Furthermore,pulses(bell-shaped)and waves fronts(kink-shaped)of the gKPPE are given.In particular,two types of approximate analytical oscillatory solutions are constructed.Besides,the error estimations between the approximate analytical oscillatory solutions and the exact solutions of the gKPPE are obtained by the homogeneity principle.Finally,the approximate analytical oscillatory solutions are compared with the numerical solutions,which shows the two types of solutions are similar.
基金supported by the Natural Science Basic Research Program of Shaanxi,China (2023-JC-QN-0053)supported by the Natural Science Foundation of China (12365009)the Natural Science Foundation of Jiangxi Province,China (20232BAB201039)
文摘We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime.Using the minimal geometric deformation(MGD)approach,we split the highly nonlinear coupled field equations into two subsystems that describe the background geometry and scalar field source,respectively.By considering the Schwarzschild-AdS metric as background geometry,we derive analytical approximate solutions of the scalar field and deformation metric functions using the homotopy analysis method(HAM),providing their analytical approximations to fourth order.Moreover,we discuss the accuracy of the analytical approximations,showing they are sufficiently accurate throughout the exterior spacetime.