Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary valu...Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.展开更多
We present a fast Poisson solver on spherical shells.With a special change of variable,the radial part of the Laplacian transforms to a constant coefficient differential operator.As a result,the Fast Fourier Transform...We present a fast Poisson solver on spherical shells.With a special change of variable,the radial part of the Laplacian transforms to a constant coefficient differential operator.As a result,the Fast Fourier Transform can be applied to solve the Poisson equation with O(N^(3) logN)operations.Numerical examples have confirmed the accuracy and robustness of the new scheme.展开更多
基金The National Natural Science Foundation of China (No.40701014)the Scientific Research Fund of Sichuan Provincial Education Department (No.09ZB081)the Research Fund of key Discipline of Xihua University:Applied Mathe-matics (No.XZD0910-09-1)
文摘Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.
基金The research of Liu was supported by the NSF grant DMS 10-11738The research of Wang was supported by National Science Council of Taiwan under grant 97-2115-M-007-005In addition,this work is also supported in part by National Center for Theoretical Sciences of Taiwan.
文摘We present a fast Poisson solver on spherical shells.With a special change of variable,the radial part of the Laplacian transforms to a constant coefficient differential operator.As a result,the Fast Fourier Transform can be applied to solve the Poisson equation with O(N^(3) logN)operations.Numerical examples have confirmed the accuracy and robustness of the new scheme.
