Abstract
One proves theorems regarding the estimates of the solutions of systems of linear algebraic equations and inequalities. On the basis of these theorems one suggests a method for estimating the norm of the inverse matrix of a system of difference equations which approximates a boundary-value problem for an integrodifferential equation. The method allows us to eliminate the restrictions which are usually imposed on the coefficients of the integrodifferential equation in order to ensure the diagonal dominance in the system of the difference equations. One considers an application to nonlinear problems.
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Literature cited
M. N. Yakovlev, “Estimates of the solutions of two-point boundary-value problems for systems of first-order integrodifferential equations and the method of lines,” J. Sov. Math.,22, No. 2 (1983).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 102, pp. 174–180, 1980.
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Yakovlev, M.N. Estimates for the solutions of systems of linear algebraic equations and their application to the investigation of the convergence of the method of finite differences. J Math Sci 22, 1270–1274 (1983). https://doi.org/10.1007/BF01460280
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DOI: https://doi.org/10.1007/BF01460280