A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations

A wavelet method is proposed for solving a class of nonlinear time-dependent partial differential equations. Following this method, the nonlinear equations are first transfoulled into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. To justify the present method, the coupled viscous Burgers' equations are solved as examples, results demonstrate that the proposed wavelet algorithm have a much better accuracy and efficiency than many existing numerical methods, and the order of convergence of such a wavelet method can even reach about 5.