| 一类二维半线性椭圆边值问题的四阶紧有限差分格式 |
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| 引用本文： | 武文佳. 一类二维半线性椭圆边值问题的四阶紧有限差分格式[J]. 上海电机学院学报, 2013, 0(1): 88-93 |
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| 作者姓名： | 武文佳 |
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| 作者单位： | 上海电机学院数理教学部,上海201306 |
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| 摘 要： | 对一类二维半线性椭圆边值问题，建立了适用于各向异性网格的四阶紧有限差分格式。用上、下解的方法讨论了有限差分解的存在唯一性，通过离散L-oo范数估计，证明了方法的收敛性和四阶精度。
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| 关 键 词： | 半线性椭圆边值问题 紧有限差分格式 四阶精度 |
Fourth-Order Compact Finite Difference Scheme for Semi-Linear Elliptic Boundary Value Problems |
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| WU Wenjia. Fourth-Order Compact Finite Difference Scheme for Semi-Linear Elliptic Boundary Value Problems[J]. JOurnal of Shanghai Dianji University, 2013, 0(1): 88-93 |
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| Authors: | WU Wenjia |
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| Affiliation: | WU Wenjia (Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China) |
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| Abstract: | A fourth-order compact finite difference scheme with non-isotropic mesh is proposed for a class of two dimensional semi-linear elliptic boundary value problems. Existence and uniqueness of the finite difference solutions are investigated using the method of upper and lower solutions. Convergence and the fourth-order accuracy of the proposed method are shown with respect to the discrete L-∞ norm. |
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| Keywords: | semi-linear elliptic boundary value problems compact finite difference scheme fourth-order accuracy |
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