Regularization of A Singularly Perturbed Elliptic PDE
نویسنده
چکیده
In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Four types of basic spectral regularization methods such as Showalter’s, Tikhonov’s, Lardy’s and Lavrentiev’s are applied to approximate the solution by introducing another large (or small) parameter. Convergence of the regularized solutions to the original are shown for such equations even though the equation involves an unbounded operator. Key-Words: Singular Perturbation, Elliptic PDE, Regularization
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