Lavrentiev regularization of a singularly perturbed elliptic PDE

摘要

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.