| 弱非线性椭圆型方程的Ritz—Galerkin解法和差分解法探讨 |
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| 引用本文： | 许福.弱非线性椭圆型方程的Ritz—Galerkin解法和差分解法探讨[J].应用数学,1993,6(4):387-391. |
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| 作者姓名： | 许福 |
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| 作者单位： | 武汉大学计算机科学 430072 |
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| 摘 要： | 本文给出了Ｒｉｔｚ－Ｇａｌｅｒｋｉｎ解法的收敛性，并对模型问题的块Ｊａｃｏｂｉ和平行弦方法进行了收敛性分析。Ｂｅｒｓ在１９６４年给出模型问题差分方法收敛性的证明，这里得到了块Ｊａｃｏｂｉ块ＳＯＲ、块Ｎｅｗｔｏｎ－Ｊａｃｏｂｉ和块Ｎｅｗｔｏｎ－Ｓｏｒ四种算法的收敛性结果。以上这些Ｊａｃｏｂｉ算法都适合于并行计算，最后给出两个具体数值例子。
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| 关 键 词： | 椭圆型方程 R－G解法 差分法 |
Analysis of Ritz-Galerkin Solutions and Discrete Solutions of MildlyNonlinear Elliptic Differential Equation |
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| Xu Fu.Analysis of Ritz-Galerkin Solutions and Discrete Solutions of MildlyNonlinear Elliptic Differential Equation[J].Mathematica Applicata,1993,6(4):387-391. |
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| Authors: | Xu Fu |
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| Abstract: | In this paper the Convergence of Ritz-Galerkin method is given,and the convergences of B-J method and parallel chord method are discussed. Bers solved the discrete method convengence of mothod problem. The convergences of B-J-M , BSOR, BNJ, BNSOR methods are obtained. All these Jacobi methods are suitable to parallel computing. In the end two numerical results are given. |
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| Keywords: | M-matrix Nonnegative subinverse Homeomorphism Block diagonal matrix Block interation |
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