Abstract
A uniform high-order method is presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems (1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (h m+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (h m+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.
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Qi-guang, W., Xiao-di, S. A uniform high-order method for a singular perturbation problem in conservative form. Appl Math Mech 13, 909–916 (1992). https://doi.org/10.1007/BF02453333
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DOI: https://doi.org/10.1007/BF02453333