Abstract
Using a functional-discrete approach, three-point difference schemes of arbitrary order of accuracy are constructed for solving the Dirichlet problem for second-order ordinary differential equations (ODE) with a small parameter multiplying the leading derivative. The uniform convergence of the schemes with respect to the small parameter is proved, and a recursive algorithm for their realization is constructed. Bibliography:4 titles.
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References
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Additional information
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 35–43.
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Grekov, L.D., Krasnikov, V.M. FD method of arbitrary uniform order of accuracy for solving singularly perturbed boundary problems for second-order ordinary differential equations. J Math Sci 77, 3420–3425 (1995). https://doi.org/10.1007/BF02367988
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DOI: https://doi.org/10.1007/BF02367988