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A second order numerical method for singularly perturbed problem with non-local boundary condition

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Abstract

The aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction–diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, 65080, Van, Turkey

    Musa Cakir

  2. Department of Mathematics, Faculty of Arts and Science, Erzincan University, 57000, Erzincan, Turkey

    Gabil M. Amiraliyev

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  1. Musa Cakir
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  2. Gabil M. Amiraliyev
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Correspondence to Musa Cakir.

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Cakir, M., Amiraliyev, G.M. A second order numerical method for singularly perturbed problem with non-local boundary condition. J. Appl. Math. Comput. 67, 919–936 (2021). https://doi.org/10.1007/s12190-021-01506-z

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  • DOI: https://doi.org/10.1007/s12190-021-01506-z

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