Abstract
In this paper, based on the idea of El-Mistikawy and Werle(1) we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
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El-Mistikawy, T.M. and M.J. Werle, Numerical method for boundary layers with blowing the exponential box scheme,AIAA. J.,16 (1978) 749–751.
Hegarty, A.F., J.J.H.Miller and E.O'Riordan, Uniform second order difference scheme for singular perturbation problems,Proc. Internat. Conf on Boundary and Interior Layers, Computational and Asymptotic Methods, June 3–6 (1980), Trinity College, Dublin, Ireland (J.J.H. Miller ed.), Boole Press, Dublin (1980), 301–305
Guo Wen, Uniform convergence of exponential box scheme for a self-adjoint problem with a small parameter, Internat. Conf. on Differential Equations, Fuzhou University (1985).
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Communicated by Lin Zong-chi
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Wen, G., Peng-cheng, L. A uniformly convergent second order difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. Appl Math Mech 10, 231–241 (1989). https://doi.org/10.1007/BF02014617
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DOI: https://doi.org/10.1007/BF02014617