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Differential equations with locally perturbed coefficients: High order error estimates for function and derivative. (English) Zbl 0853.65084
Authors’ abstract: High-order error estimates are obtained for both function and derivative when the coefficients and right-hand side of a given initial or boundary value problem are replaced by piecewise polynomial functions. These estimates are given for partition points and also continuously on subintervals. Based on our results for the linear case, we propose a new technique to solve nonlinear differential equations. Numerical examples demonstrates the accuracy of our estimates.

MSC:
65L70 Error bounds for numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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