In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependen...In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.展开更多
In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential e...In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential equations with initial boundary value (IBVP). According to boundary condition, the initial condition is expanded into a Fourier series. After that, the IBVP is transformed to an iterative relation in K-domain. The series solution or exact solution can be obtained. The rationality and practicability of the algorithm FDTM are verified by comparisons of the results obtained by FDTM and the existing analytical solutions.展开更多
Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary elem...The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.展开更多
文摘In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.
文摘In this paper, a new Fourier-differential transform method (FDTM) based on differential transformation method (DTM) is proposed. The method can effectively and quickly solve linear and nonlinear partial differential equations with initial boundary value (IBVP). According to boundary condition, the initial condition is expanded into a Fourier series. After that, the IBVP is transformed to an iterative relation in K-domain. The series solution or exact solution can be obtained. The rationality and practicability of the algorithm FDTM are verified by comparisons of the results obtained by FDTM and the existing analytical solutions.
基金supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
基金This project is supported by National Natural Science Foundation of China
文摘The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.
