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arXiv · 1806.10398

Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data

Jose Luis Gracia·Eugene O'Riordan
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Abstract

Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible bound\-ary-initial data are generated, The method involves combining the computational solution of a classical finite difference operator on a tensor product of two piecewise-uniform Shishkin meshes with an analytical function that captures the local nature of the incompatibility. A proof is given to show almost first order parameter-uniform convergence of these numerical/analytical approximations. Numerical results are given to illustrate the theoretical error bounds.

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Jose Luis Gracia, Eugene O'Riordan. 2018-06-27. Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data. https://arxiv.org/abs/1806.10398

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