| 二维半线性抛物方程的一类线性化交替方向隐格式 |
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| 引用本文： | 张磊,王同科. 二维半线性抛物方程的一类线性化交替方向隐格式[J]. 天津师范大学学报(自然科学版), 2009, 29(4): 14-18 |
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| 作者姓名： | 张磊 王同科 |
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| 作者单位： | 天津师范大学,数学科学学院,天津,300387 |
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| 摘 要： | 针对二维半线性抛物型方程初边值问题提出了一类形式非常简单的线性化二层Peaceman-Rachford交替方向差分格式,利用离散能量方法证明了格式在空间和时间方向按照离散L2范数均具有二阶精度.数值例子验证了格式的有效性.
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| 关 键 词： | 二维半线性抛物方程 P-R交替方向差分格式 收敛性分析 |
A linearized alternating direction implicit difference scheme for two-dimensional semilinear parabolic equations |
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| ZHANG Lei,WANG Tongke. A linearized alternating direction implicit difference scheme for two-dimensional semilinear parabolic equations[J]. Journal of Tianjin Normal University(Natural Science Edition), 2009, 29(4): 14-18 |
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| Authors: | ZHANG Lei WANG Tongke |
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| Affiliation: | (College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China) |
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| Abstract: | A simple linearized two level Peaceman-Rachford alternating direction implicit difference scheme is presented for two-dimensional semilinear parabolic equations with initial and boundary conditions. It is proved that the scheme has second order accuracy with respect to discrete L^2 norm by discrete energy method. The numerical example illustrates the validity of the scheme. |
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| Keywords: | two-dimensional semilinear parabolic equations Peaceman-Rachford alternating direction implicit difference scheme convergence analysis |
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