Summary
A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems.
Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
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Israeli, M., Ungarish, M. Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations. Numer. Math. 39, 309–324 (1982). https://doi.org/10.1007/BF01407865
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DOI: https://doi.org/10.1007/BF01407865