Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a ...Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.展开更多
In this paper,we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations.This method uses the Hermite basis fu...In this paper,we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations.This method uses the Hermite basis functions,by which physical quantities are approximatedwith their values and derivatives associatedwith Gaussian points.The convergence rate with order O(h4+t2)and the stability of the scheme are proved.Conservation properties are shown in both theory and practice.Extensive numerical experiments are presented to validate the numerical study under consideration.展开更多
The equations of large deformations of laminated orthotropic spherical shellsare derived. The effects of transverse shear deformation and initial imperfection are considered. on this basis. the semi-analytical solutio...The equations of large deformations of laminated orthotropic spherical shellsare derived. The effects of transverse shear deformation and initial imperfection are considered. on this basis. the semi-analytical solution of the axisymrnetric snap-throughbuckling of laminated orthotropic shallow spherical shells under uniform pressure is obtained using orthogonal collocation method. The effects of material parameters, structuralparameters, initial imperfection and transverse shear deformation are discussed.展开更多
An approach for the simulation and optimization of continuous catalyst-regenerative process of reforming is proposed in this paper.Compared to traditional method such as finite difference method,the orthogonal colloca...An approach for the simulation and optimization of continuous catalyst-regenerative process of reforming is proposed in this paper.Compared to traditional method such as finite difference method,the orthogonal collocation method is less time-consuming and more accurate,which can meet the requirement of real-time optimization(RTO).In this paper,the equation-oriented method combined with the orthogonal collocation method and the finite difference method is adopted to build the RTO model for catalytic reforming regenerator.The orthogonal collocation method was adopted to discretize the differential equations and sequential quadratic programming(SQP)algorithm was used to solve the algebraic equations.The rate constants,active energy and reaction order were estimated,with the sum of relative errors between actual value and simulated value serving as optimization objective function.The model can quickly predict the fields of component concentration,temperature and pressure inside the regenerator under different conditions,as well as the real-time optimized conditions for industrial reforming regenerator.展开更多
In this paper, the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived. The nonlinear static and dynamic response and dynamic buckling of sha...In this paper, the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived. The nonlinear static and dynamic response and dynamic buckling of shallow spherical shells with circular hole on elastically restrained edge are investigated. By using the orthogonal point collocation method for space and Newmarh-β scheme for time, the displacement functions are separated and the nonlinear differential equations are replaced by linear algebraic equations to seek solutions. The numerical results are presented for different cases and compared with available data.展开更多
文摘Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.
文摘In this paper,we present the use of the orthogonal spline collocation method for the semi-discretization scheme of the one-dimensional coupled nonlinear Schrödinger equations.This method uses the Hermite basis functions,by which physical quantities are approximatedwith their values and derivatives associatedwith Gaussian points.The convergence rate with order O(h4+t2)and the stability of the scheme are proved.Conservation properties are shown in both theory and practice.Extensive numerical experiments are presented to validate the numerical study under consideration.
文摘The equations of large deformations of laminated orthotropic spherical shellsare derived. The effects of transverse shear deformation and initial imperfection are considered. on this basis. the semi-analytical solution of the axisymrnetric snap-throughbuckling of laminated orthotropic shallow spherical shells under uniform pressure is obtained using orthogonal collocation method. The effects of material parameters, structuralparameters, initial imperfection and transverse shear deformation are discussed.
基金This work was supported by the Science and Technology Development Project of SINOPEC,China(No.319026).
文摘An approach for the simulation and optimization of continuous catalyst-regenerative process of reforming is proposed in this paper.Compared to traditional method such as finite difference method,the orthogonal collocation method is less time-consuming and more accurate,which can meet the requirement of real-time optimization(RTO).In this paper,the equation-oriented method combined with the orthogonal collocation method and the finite difference method is adopted to build the RTO model for catalytic reforming regenerator.The orthogonal collocation method was adopted to discretize the differential equations and sequential quadratic programming(SQP)algorithm was used to solve the algebraic equations.The rate constants,active energy and reaction order were estimated,with the sum of relative errors between actual value and simulated value serving as optimization objective function.The model can quickly predict the fields of component concentration,temperature and pressure inside the regenerator under different conditions,as well as the real-time optimized conditions for industrial reforming regenerator.
文摘In this paper, the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived. The nonlinear static and dynamic response and dynamic buckling of shallow spherical shells with circular hole on elastically restrained edge are investigated. By using the orthogonal point collocation method for space and Newmarh-β scheme for time, the displacement functions are separated and the nonlinear differential equations are replaced by linear algebraic equations to seek solutions. The numerical results are presented for different cases and compared with available data.
