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Browsing by Author "Xu, Aimin"

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    An Almost Second Order Uniformly Convergent Scheme for a Singularly Perturbed Initial Value Problem
    (Springer, 2014) Cen, Zhongdi; Erdogan, Fevzi; Xu, Aimin
    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.