解偏微分方程的多步-小波-Galerkin方法  

A multi-step wavelet Galerkin method for partial differential equations

作　　者：邓小炎[1] 朱静芬[2] 

机构地区：[1]华中农业大学理学院,湖北武汉430070 [2]浙江大学理学院数学系,浙江杭州310028

出　　处：《高校应用数学学报（A辑）》2007年第3期332-342,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10371135)

摘　　要：推广Lax-Wendroff多步方法,建立一类新的显式和隐式相结合的多步格式,并以此为基础提出了一类显隐多步-小波-Galerkin方法,可以用来求解依赖时间的偏微分方程.不同于Taylor-Galerkin方法,文中的方案在提高时间离散精度时不包含任何新的高阶导数.由于引入了隐式部分,与传统的多步方法相比该方案有更好的稳定性,适合于求解非线性偏微分方程,理论分析和数值例子都说明了方法的有效性.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.

关 键 词：多步方法 小波-Galerkn 热传导方程 非线性Burgers方程 

分 类 号：O241.82[理学—计算数学]