TY  - EJOU
AU  - Liu, Xiaojing 
AU  - Wang, Jizeng 
AU  - Zhou, Youhe 

TI  - A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2013
VL  - 94
IS  - 3
SN  - 1526-1506

AB  - A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed 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.
KW  - modified wavelet Galerkin method
KW  -  Runge-Kutta method
KW  -  nonlinear time-dependent partial differential equations
KW  -  Burgers’ equation

DO  - 10.32604/cmes.2013.094.225