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A comparative study of discretization techniques for augmented Urysohn type nonlinear functional Volterra integral equations and their convergence analysis

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  • Bhat, Imtiyaz Ahmad
  • Mishra, Lakshmi Narayan

Abstract

This article considers the nonlinear functional Volterra integral equation, the Urysohn type class of nonlinear integral equations. In an approach based on the Picard iterative method, the solution's existence and uniqueness are demonstrated. The trapezoidal and Euler discretization methods are used for the approximation of a numerical solution, and a nonlinear algebraic system of equations is obtained. The first and second order of convergence for the Euler and the trapezoidal methods respectively to the solution is manifested by employing the Gronwall inequality and its discrete form. A new Gronwall inequality is devised in order to prove the trapezoidal method's convergence. Finally, some numerical examples are provided which attest to the application, effectiveness, and reliability of the methods.

Suggested Citation

  • Bhat, Imtiyaz Ahmad & Mishra, Lakshmi Narayan, 2024. "A comparative study of discretization techniques for augmented Urysohn type nonlinear functional Volterra integral equations and their convergence analysis," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000274
    DOI: 10.1016/j.amc.2024.128555
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    References listed on IDEAS

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    1. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
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