A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems
نویسندگان
چکیده
A coupled system of two singularly perturbed linear reaction–diffusion two-point boundary value problems is examined. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analysed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh central differencing is proved to be almost first-order accurate, uniformly in both small parameters. Supporting numerical results are presented for a test problem.
منابع مشابه
Pre-publicaciones Del Seminario Matematico 2008 an Almost Second Order Uniformly Convergent Method for Parabolic Singularly Perturbed Reaction- Diffusion Systems an Almost Second Order Uniformly Convergent Method for Parabolic Singularly Perturbed Reaction-diffusion Systems *
In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. The small values of the diffusion parameters, in general, cause that the solution has boundary layers at the ends of the spatial domain. To obtain an efficient approximation of the solution we propose a numerical method combining the Crank-Nicolson m...
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