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An almost second order uniformly convergent scheme for a singularly perturbed initial value problem

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Abstract

In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midpoint upwind scheme on the coarse mesh. It is proved that the scheme is almost second-order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiment supports these theoretical results.

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, People’s Republic of China

    Zhongdi Cen & Aimin Xu

  2. Department of Mathematics, Faculty of Sciences, Yuzuncuyil University, 65080, Van, Turkey

    Fevzi Erdogan

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  1. Zhongdi Cen
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  2. Fevzi Erdogan
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  3. Aimin Xu
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Correspondence to Zhongdi Cen.

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Cen, Z., Erdogan, F. & Xu, A. An almost second order uniformly convergent scheme for a singularly perturbed initial value problem. Numer Algor 67, 457–476 (2014). https://doi.org/10.1007/s11075-013-9801-0

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  • DOI: https://doi.org/10.1007/s11075-013-9801-0

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