A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations
A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations
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DOI：
10.3970/cmes.2013.094.225
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发表时间：
2013-08
影响因子：
2.4
通讯作者：
Xiaojing Liu;Jizeng Wang;Youhe Zhou
中科院分区：
文献类型：
--
作者：
Xiaojing Liu;Jizeng Wang;Youhe Zhou
提出了一种求解一类非线性时变偏微分方程的小波方法。在此基础上，首先利用作者提出的改进小波Galerkin方法将非线性方程组化为常微分方程组。然后，经典的四阶显式龙格-库塔法求解所得到的常微分方程组。以粘性耦合Burgers方程为例进行了数值求解，结果表明，所提出的小波算法比现有的数值方法具有更高的精度和效率，其收敛阶可达5阶左右.
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.