For the numerical solution of boundary-value problems on the semiaxis for second-order nonlinear ordinary differential equations, an exact three-point difference scheme is constructed and substantiated. Under the conditions of existence and uniqueness of solution of a boundary-value problem, we prove the existence and uniqueness of solution of the exact three-point difference scheme and convergence of the method of successive approximations for its solution.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 75–86, October–December, 2010.
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Kutniv, M.V., Pazdrii, O.I. Exact three-point difference scheme for a nonlinear boundary-value problem on the semiaxis. J Math Sci 181, 383–400 (2012). https://doi.org/10.1007/s10958-012-0692-8
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DOI: https://doi.org/10.1007/s10958-012-0692-8