A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems-中国期刊网

摘要 Asystemofm(≥2)linearconvection-diffusiontwo-pointboundaryvalueproblemsisexamined,wherethediffusiontermineachequationismultipliedbyasmallparameterεandtheequationsarecoupledthroughtheirconvectiveandreactivetermsviamatricesBandArespectively.Thissystemisingeneralsingularlyperturbed.Unlikethecaseofasingleequation,itdoesnotsatisfyaconventionalmaximumprinci-ple.CertainhypothesesareplacedonthecouplingmatricesBandAthatensureexis-tenceanduniquenessofasolutiontothesystemandalsopermitboundarylayersinthecomponentsofthissolutionatonlyoneendpointofthedomain;thesehypothesescanberegardedasastrongformofdiagonaldominanceofB.Thissolutionisdecomposedintoasumofregularandlayercomponents.Boundsareestablishedonthesecompo-nentsandtheirderivativestoshowexplicitlytheirdependenceonthesmallparameterε.Finally,numericalmethodsconsistingofupwindingonpiecewise-uniformShishkinmeshesareprovedtoyieldnumericalsolutionsthatareessentiallyfirst-orderconver-gent,uniformlyinε,tothetruesolutioninthediscretemaximumnorm.NumericalresultsonShishkinmeshesarepresentedtosupportthesetheoreticalbounds.

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A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems

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A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems

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