A Patched Mesh Method for Singularly Perturbed Reaction-Diffusion Equations

机译：奇摄动反应扩散方程的修补网格方法

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摘要

A singularly perturbed elliptic problem of reaction-diffusion type is examined. The solution is decomposed into a sum of a regular component, boundary layer components and corner layer components. Numerical approximations are generated separately for each of these components. These approximations are patched together to form a global approximation to the solution of the continuous problem. An asymptotic error bound in the pointwise maximum norm is established; whose dependence on the values of the singular perturbation parameter is explicitly identified. Numerical results are presented to illustrate the performance of the numerical method.

机译：研究了反应扩散型的奇摄动椭圆问题。该解被分解为规则分量，边界层分量和角层分量的总和。对于这些组件中的每个组件，分别生成数值近似值。将这些近似值修补在一起，以形成对连续问题的解的全局近似值。建立在点最大范数内的渐近误差；明确识别其对奇异摄动参数值的依赖性。数值结果表明了数值方法的性能。

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来源
《Bail 2008 - boundary and interior layers》|2008年|117-127|共11页
会议地点 Limerick(IE)
作者
C. de Falco; E. ORiordan;
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作者单位

School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland;

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会议组织
原文格式 PDF
正文语种 eng
中图分类工程数学;
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3. Robust computational methods for a coupled system of singularly perturbed reaction-diffusion equations with discontinuous source term [J] . Mahabub Basha Pathan, Shanthi Vembu Journal of Modern Methods in Numerical Mathematics . 2015,第2期

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5. Numerical methods for singularly perturbed boundary value problems and singularly perturbed equations. [D] . Savin, Igor. 2010

机译：奇摄动边值问题和奇摄动方程的数值方法。
6. Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations [O] . Gabil M. Amiraliyev, Aysenur Ucar 2013

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7. Asymptotic numerical methods for singularly perturbed fourth-order ordinary differential equations of reaction-diffusion type [O] . Shanthi V., Ramanujam N. 2003

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A Patched Mesh Method for Singularly Perturbed Reaction-Diffusion Equations

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