Study Of High Accuracy Compact Finite Difference Scheme For GRRLW Equation And GL Equation

No matter in theory or in practical application, the numerical method for solving the partial differential equation is an important branch of modem mathematics. Because most of them can't obtain the accurate solution, so the method for solving the approximation is the most worthy of application. In this paper, we study two classes of the initial-boundary value problem of nonlinear partial differential equation by the finite difference method.First of all,we construct a conservation difference scheme with two parameters ?,?for the one dimensional General Rosenau-RLW (GRRLW) equation. Based on energy analysis method, it is proved that energy conservation properties of the finite difference scheme and the numerical solution is uniquely solvable, the convergence and unconditional stability of the difference schemes are obtained,and its numerical convergence order is O(?2 +h2) in the L? -norm.Secondly, we construct a higher order conservation compact difference scheme for the one dimensional General Rosenau-RLW (GRRLW) equation. Based on energy analysis method, it is proved that energy conservation properties of the finite difference scheme and the numerical solution is uniquely solvable, the convergence and unconditional stability of the difference schemes are obtained, and its numerical convergence order is O(?2 +h4) in the L? -norm.Finally, we construct a higher order compact difference scheme for the two dimensional Ginzbung-Landau (GL) equation. Based on energy analysis method, it is proved that the numerical solution is uniquely solvable and its prior estimation is obtained.The convergence and stability of the difference schemes are obtained,and its numerical convergence order is o(?2 + h4) in the H1 -norm.The numerical experiments are carried out respectively for schemes. Numerical experiment results show that the theory is accurate and the schemes are efficient and reliable.