重调和方程Legendre小波法
首发时间:2019-06-13
摘要:重调和方程在流体分析、薄板弯曲等问题上有着重要的应用,近些年来已经提出了多种数值解法。本文提出了求解一维和一类二维重调和方程的Legendre小波法。Legendre小波具有正交性,小支集性,以及区域的有界性和小波函数的可计算性。文中利用了Legendre小波积分算子矩阵求解,大大降低了运算的复杂度和较少占用内存空间,使运算过程简单易行。同时得到了高精度的数值解,最后本文给出的数值算例表明了该方法的可行性和有效性。
关键词: 重调和方程; Legendre小波; 算子矩阵; 数值解
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Legendre wavelets method for solving biharmonic equation
Abstract:The biharmonic equation has important applications in fluid analysis, sheet bending, etc. Various numerical solutions have been proposed in recent years. In this paper, we propose a Legendre wavelet method for solving one-dimensional and two-dimensional biharmonic equations. The Legendre wavelet has orthogonality, small support, and the boundedness of the region and the computability of the wavelet function. The paper uses the Legendre wavelet integral operator matrix to solve the problem, which greatly reduces the computational complexity and less memory space, making the operation process simple and easy. At the same time, the numerical solution of high precision is obtained. Finally, the numerical examples are given in this paper to show the feasibility and effectiveness of the method.
Keywords: biharmonic equation Legendre wavelets operational matrix numerical solution
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