A multi-step wavelet Galerkin method for partial differential equations
Xiaoyan Deng · 2007
A new explicit-implicit multi-step scheme by extending multi-step Lax-Wendroff scheme is constructed,and the concept of explicit-implicit multi-step wavelet Galerkin method which aims to solve time-dependent partial differential equations is introduced.Unlike in Taylor Galerkin methods,the presented scheme does not contain any new higher order derivatives,but improves the order of approximating accuracy in time.Comparing to conventional multi-step method,the scheme in the paper has better stability which makes it suitable for solving linear and non-linear partial differential equations.Theoretical analysis and numerical results illustrate the versatility and effectiveness of the proposed scheme.