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Superconvergence analysis of multistep collocation method for delay functional integral equations. (English) Zbl 1424.65099

Summary: In this paper, we present a review of the multistep collocation method for delay Volterra integral equations (DVIEs) from [the author, Sahand Commun. Math. Anal. 3, No. 2, 47–65 (2016; Zbl 1365.65281)] and then, we study the superconvergence analysis of the multistep collocation method for DVIEs. Some numerical examples are given to confirm our theoretical results.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34K06 Linear functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65R20 Numerical methods for integral equations
45D05 Volterra integral equations

Citations:

Zbl 1365.65281
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