Analysis of Immersed Interface Difference Schemes for Reaction-diffusion Problems with Singular Own Sources
Analysis of Immersed Interface Difference Schemes for Reaction-diffusion Problems with Singular Own Sources
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DOI：
10.2478/cmam-2003-0017
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Kandilarov;L. Vulkov
中科院分区：
文献类型：
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作者：
J. Kandilarov;L. Vulkov
摘要本文分析了具有奇异自线性和非线性源的一维反应扩散方程的浸入界面差分格式。基于极大值原理，推导了无穷范数下的误差界。使用渐近误差展开分析方法，得到了更清晰的边界和更详细的误差结构。数值算例验证了理论结果。
Abstract This paper analyzes immersed interface difference schemes for onedimensional reaction-diffusion equations with singular own linear and nonlinear sources. Error bounds in the infinity norm based on the maximum principle are derived. Sharper bounds and a more detailed structure of the error are obtained using the asymptotic error expansion analysis method. Numerical examples confirm the theoretical results.