Please use this identifier to cite or link to this item: http://hdl.handle.net/11717/7629
Title: Lavrentiev regularization of a singularly perturbed elliptic PDE
Authors: Sheela, S.
Singh, A.
Keywords: Boundary value problems
Diffusion
Perturbation techniques
Lavrentiev regularization
Partial differential equations
Issue Date: 2004
Citation: Applied Mathematics and Computation, 148(1), 189-205
Abstract: This paper considers a reaction-diffusion equation with a small parameter multiplied with the derivatives. Considering this as an ill-posed problem, Lavrentiev regularization method is used to formulate the related well-posed problem. Pointwise a priori estimates of the regularized solutions and of the regularization error are also derived. The regularized equations are solved numerically via the central difference scheme. It is suggested that any other suitable discretization might also be used to solve the regularized problems. Also it is found that with a comparatively small number of grid points, the numerical solution of the regularized equation comes up as a good approximation to the original solution. ? 2002 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/S0096-3003(02)00837-8
http://hdl.handle.net/11717/7629
ISSN: 963003
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