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On generalized multistep collocation methods for Volterra integro-differential equations

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  • Li, Haiyang
  • Ma, Junjie

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.

Suggested Citation

  • Li, Haiyang & Ma, Junjie, 2024. "On generalized multistep collocation methods for Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 399-412.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:399-412
    DOI: 10.1016/j.matcom.2024.07.019
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    References listed on IDEAS

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    1. Behera, S. & Saha Ray, S., 2022. "Two-dimensional wavelets scheme for numerical solutions of linear and nonlinear Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 332-358.
    2. Chen, Hao & Ma, Junjie, 2022. "Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolation," Applied Mathematics and Computation, Elsevier, vol. 414(C).
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