Uniformly convergent difference schemes for a singularly perturbed third order boundary value problem |
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Institution: | 1. College of Biochemical Engineering, Beijing Union University, Beijing 100023, China;2. College of Sciences, North China University of Technology, Beijing 100144, China |
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Abstract: | In this paper we consider a numerical approximation of a third order singularly perturbed boundary value problem by an upwind finite difference scheme on a Shishkin mesh. The behavior of the solution, and the stability of the continuous problem are discussed. The proof of the uniform convergence of the proposed numerical method is based on the strongly uniform stability and a weak consistency property of the discrete problem. Numerical experiments verify our theoretical results. |
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Keywords: | Singular perturbation Boundary value problem Layer-adapted meshes Finite difference method |
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