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An Iterative Tikhonov Regularization for Solving Singularly Perturbed Elliptic PDE

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Abstract

In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We consider a regularized iterative method for solving such problems. Convergence analysis and error estimate are derived. The regularization parameter is chosen according to an a priori strategy. We give numerical results to illustrate that the method is implementable compared with numerical methods such as Shishkin and finite element schemes. The study demonstrates that the iterated regularized scheme can be considered as an alternate method for solving singularly perturbed elliptical problems.

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Authors and Affiliations

  1. School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala (PO), Vithura, Thiruvananthapuram, Kerala, 695 551, India

    M. P. Rajan

  2. School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, CET Campus, Thiruvananthapuram, Kerala, 695 016, India

    G. D. Reddy

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  1. M. P. Rajan
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  2. G. D. Reddy
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Correspondence to M. P. Rajan.

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Rajan, M.P., Reddy, G.D. An Iterative Tikhonov Regularization for Solving Singularly Perturbed Elliptic PDE. Mediterr. J. Math. 14, 180 (2017). https://doi.org/10.1007/s00009-017-0980-0

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  • DOI: https://doi.org/10.1007/s00009-017-0980-0

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