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The extended generalized Störmer–Cowell methods for second-order delay boundary value problems

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  • Li, Cui
  • Zhang, Chengjian

Abstract

This paper deals with the numerical solutions of second-order delay boundary value problems (DBVPs). The generalized Störmer–Cowell methods (GSCMs) for second-order initial value problems, proposed by Aceto et al. (2012), are extended to solve the second-order DBVPs. The existence and uniqueness criterion of the methods is derived. It is proved under the suitable conditions that an extended GSCM is stable, and convergent of order p whenever this method has the consistent order p. The numerical examples illustrate efficiency and accuracy of the methods. Moreover, a comparison between the extended GSCMs and the boundary value methods of first-order BVPs is given. The numerical result shows that the extended GSCMs are comparable.

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  • Li, Cui & Zhang, Chengjian, 2017. "The extended generalized Störmer–Cowell methods for second-order delay boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 87-95.
    • Handle: RePEc:eee:apmaco:v:294:y:2017:i:c:p:87-95
    DOI: 10.1016/j.amc.2016.09.006
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    1. Chen, Hao & Yang, Yeru, 2021. "Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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