小波法求解非线性分数阶偏微分方程  

Wavelet Method for Solving Nonlinear Partial Differential Equations of Fractional Order

作　　者：郝玲[1] 牛红玲[1] 成福伟[2] 尹建华[1] 

机构地区：[1]河北民族师范学院数学与计算机系,河北承德067000 [2]河北民族师范学院科研处,河北承德067000

出　　处：《河北师范大学学报（自然科学版）》2013年第5期453-457,共5页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金(A2011205092)

摘　　要：考虑一类非线性分数阶偏微分方程的数值解法.Haar小波具有正交性,区域的有界性以及小波函数的可计算性.将Haar小波与算子矩阵思想进行结合,恰当离散初始方程,使非线性分数阶偏微分方程转换为非线性代数方程组,进而可以编程求解,最后,数值算例验证了方法的有效性.In this paper, we consider the numerical method for a class of nonlinear partial differential equations of fractional order. The Haar wavelet is known to have a small bottle, orthogonality,and the computability of the wavelet function. We combine the Haar wavelet with the operational matrix and then discretize these equations. So the original problem is transformed into a nonlinear system of algebraic equations,which is now solvable by using software. Finally, a numerical example shows that this approach is effective.

关 键 词：非线性 分数阶导数 HAAR小波 算子矩阵 数值解 

分 类 号：O241.8[理学—计算数学]