An economical difference scheme is proposed to solve convection-diffusion equations. The transport term is discretized by the method of characteristics, then the difference system are docomposed to several problems of...An economical difference scheme is proposed to solve convection-diffusion equations. The transport term is discretized by the method of characteristics, then the difference system are docomposed to several problems of individual variable using alternating direction method. Two kinds of interpolation operators are supplied for the technique of characteristics. The stability and convergence are analysed by energy method. Numerical result implies that this scheme has better accuracy and higher efficiency then the standard scheme of two-order center difference quotient.展开更多
B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-...B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.展开更多
The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in whic...The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in this paper belongs to the second order parabolic equations with non-negative characteristic form, namely, there exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some a priori regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in this paper. The results can be extended to more general degenerate parabolic equations.展开更多
Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg...Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Algorithm to prove the stability and convergence of the approximations.展开更多
The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudos...The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.展开更多
文摘An economical difference scheme is proposed to solve convection-diffusion equations. The transport term is discretized by the method of characteristics, then the difference system are docomposed to several problems of individual variable using alternating direction method. Two kinds of interpolation operators are supplied for the technique of characteristics. The stability and convergence are analysed by energy method. Numerical result implies that this scheme has better accuracy and higher efficiency then the standard scheme of two-order center difference quotient.
文摘B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.
基金supported by the National Natural Science Foundation of China(Nos.11061018,11261029)the Youth Foundation of Lanzhou Jiaotong University(No.2011028)+1 种基金the Long Yuan Young Creative Talents Support Program(No.252003)the Joint Funds of the Gansu Provincial Natural Science Foundation of China(No.1212RJZA043)
文摘The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in this paper belongs to the second order parabolic equations with non-negative characteristic form, namely, there exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some a priori regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in this paper. The results can be extended to more general degenerate parabolic equations.
文摘Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Algorithm to prove the stability and convergence of the approximations.
文摘The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual onesl is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.
