用分段多项式加权残差法求解时变偏微分方程

Meraj Alam, Md. Shafiqul Islam
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引用次数: 2

摘要

采用伽辽金加权残差(GWR)方法对一维热波方程作为初值和边值问题进行数值求解。利用Bernstein、Bernoulli和Legendre三种特殊类型的分段多项式作为基函数来求解这些IBVPs。用该方法对几个算例进行了测试,并与现有方法的解进行了比较。本文的数值计算结果与精确解吻合较好。达卡大学学报,67(1):5-12,2019 (1)
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Numerical Solutions of Time Dependent Partial Differential Equations Using Weighted Residual Method With Piecewise Polynomials
We use Galerkin weighted residual (GWR) method to solve one dimensional heat and wave equations as initial and boundary value problems (IBVPs) numerically. Three special types of piecewise polynomials namely: Bernstein, Bernoulli and Legendre polynomials are used as basis functions to solve these IBVPs. A few examples are tested by the proposed method and then the results are compared with the solutions found in other existing methods. The numerical results obtained in this paper are in good agreement with the exact solutions. Dhaka Univ. J. Sci. 67(1): 5-12, 2019 (January)
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