The Study Of The Cosine-based Differential Quadrature Method For Solving Numerically Several Nonlinear Evolution Equations

With the development of nonlinear science, solving the nonlinear evolution equations has become a hot question to a great number of researchers who study physics, mechanics, geoscience, life sciences, applied mathematics and engineering technique. At the present, although a number of methods are proposed to look for the exact solutions of nonlinear evolution equations, unfortunately, in most cases, we can only obtain their analytical or approximate solutions for some special cases, but we can’t obtain the widely used solutions. Along with the development of computational physics, the numerical methods for solving nonlinear partial differential equations on naturally become a kind of very important method. In this dissertation, we apply the Differential Quadrature Method to solve some of the (1+1)-dimensional nonlinear evolution equations, and some mainly works as follow:1. Cosine expansion-based differential quadrature method for numerical solutions of the RLW equation. The validity and accuracy of Cosine expansion-based differential quadrature method for solving nonlinear partial differential equations are verified by numerical experiments.2. Cosine expansion-based differential quadrature method for numerical solutions of the Kuramoto-Sivashinsky equation. By sloving the RLW equation with some different initial conditions, the results show that the numerical solutions are highly accurate to the different initial conditions.3. Cosine expansion-based differential quadrature method for numerical solutions of the KdV-Burgers equation. By numerical calculation, we obtained the highly accurate numerical solutions, and verified the validity of the CDQM.