Abstract
Some sufficient conditions are considered, under which the solutions of a class of incompletely exponentially fitted difference schemes converge uniformly in ɛ, with orders one and two, to the solution of the singular perturbation problem: ɛu″+a(x)u′−b(x)u=f(x), for 0<x<1, u(0), u(1) given. ɛε(0,1], a(x)>a>0, b(x)≥0. From these conditions an incompletely exponentially fitted second-order scheme is derived. Finally, the results of some numerical experiments are given.
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Communicated by Lin Zong-chi
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Peng-cheng, L., Guang-fu, S. A class of incompletely exponentially fitted difference schemes for a singular perturbation problem. Appl Math Mech 8, 1133–1143 (1987). https://doi.org/10.1007/BF02450908
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DOI: https://doi.org/10.1007/BF02450908