In this paper, a new elimination of finite differential equations has been discussed. It applies the numerical direct iteration to obtain the residual equations, in which the number of unknowns has been reduced greatl...In this paper, a new elimination of finite differential equations has been discussed. It applies the numerical direct iteration to obtain the residual equations, in which the number of unknowns has been reduced greatly. The solution process is simple and efficient, and the solution is exact展开更多
In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform...In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.展开更多
文摘In this paper, a new elimination of finite differential equations has been discussed. It applies the numerical direct iteration to obtain the residual equations, in which the number of unknowns has been reduced greatly. The solution process is simple and efficient, and the solution is exact
文摘In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.
