On generalized multistep collocation methods for Volterra integro-differential equations

Haiyang Li and Junjie Ma

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 399-412

Abstract: We propose a modification of multistep collocation methods for Volterra integro-differential equations, an important type of Volterra equations including the derivative and integral of the unknown solution. Superimplicit interpolations are employed to represent the collocation polynomial. The investigation on the existence and convergence of the collocation solution shows that the proposed approach is able to attain a high convergence rate without adding collocation points. Besides, the stability analysis of the proposed collocation method indicates that its stability region can be enlarged by adjusting interpolation nodes. Several numerical experiments are provided to confirm theoretical results.

Keywords: Volterra integro-differential equation; Collocation method; Multistep; Convergence analysis; Stability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:399-412

DOI: 10.1016/j.matcom.2024.07.019

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