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Tikhonov Regularization of a Two-point Boundary Value Problem where the Highest Order Term is Multiplied by a Small Parameter
Abstract
This paper considers a singularly perturbed two-point boundary value problem where the highest order derivative is multiplied by a small positive parameter. The original solution for this kind of problem does not converge uniformly to the reduced solution. Hence the problem becomes an ill-posed one. Therefore, the applicability of Tikhonov regularization technique to solve this type of problem is explored. A priori and a posteriori parameter
choice strategies for the regularization parameter are also discussed. Numerical experiments show that regularized solution improves the accuracy of the computed solution.
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