Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order Delay-Integro-Differential Equations

Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order... This paper deals with the numerical solutions of nonlinear boundary value problems (BVPs) of second-order delay-integro-differential equations. The generalized Störmer–Cowell methods (GSCMs), combined with the compound quadrature rules, are extended to solve this class of BVPs. It is proved under some suitable conditions that the extended GSCMs are uniquely solvable, stable and convergent of order $$\min \{p,q\}$$ min { p , q } , where p, q are consistent order of the GSCMs and convergent order of the compound quadrature rules, respectively. Several numerical examples are presented to illustrate the proposed methods and their theoretical results. Moreover, a numerical comparison with the existed methods is also given, which shows that the extended GSCMs are comparable in numerical precision and computational cost. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

Generalized Störmer–Cowell Methods for Nonlinear BVPs of Second-Order Delay-Integro-Differential Equations

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0491-y
Publisher site
See Article on Publisher Site

Abstract

This paper deals with the numerical solutions of nonlinear boundary value problems (BVPs) of second-order delay-integro-differential equations. The generalized Störmer–Cowell methods (GSCMs), combined with the compound quadrature rules, are extended to solve this class of BVPs. It is proved under some suitable conditions that the extended GSCMs are uniquely solvable, stable and convergent of order $$\min \{p,q\}$$ min { p , q } , where p, q are consistent order of the GSCMs and convergent order of the compound quadrature rules, respectively. Several numerical examples are presented to illustrate the proposed methods and their theoretical results. Moreover, a numerical comparison with the existed methods is also given, which shows that the extended GSCMs are comparable in numerical precision and computational cost.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jul 4, 2017

References

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