In this work we use the He’s variational iteration method and Adomian decomposition method to solution N-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) Equation.
Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking ...Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.展开更多
We consider the generalized integrable fifth order nonlinear Korteweg-de Vries （fKdV） equation. The extended Tanh method has been used rigorously, by com- putational program MAPLE, for solving this fifth order nonli...We consider the generalized integrable fifth order nonlinear Korteweg-de Vries （fKdV） equation. The extended Tanh method has been used rigorously, by com- putational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact solutions are found for the two fifth order KdV-type equations given by the Caudrey-Dodd-Gibbon equation and the another fifth order equation. The obtained solutions include solitary wave solution for both the two equations.展开更多
文摘In this work we use the He’s variational iteration method and Adomian decomposition method to solution N-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) Equation.
基金Supported by the National Natural Science Foundation of China(11602262)
文摘Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.
文摘We consider the generalized integrable fifth order nonlinear Korteweg-de Vries （fKdV） equation. The extended Tanh method has been used rigorously, by com- putational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact solutions are found for the two fifth order KdV-type equations given by the Caudrey-Dodd-Gibbon equation and the another fifth order equation. The obtained solutions include solitary wave solution for both the two equations.
