 A comparative study of discretization techniques for augmented Urysohn type nonlinear functional Volterra integral equations and their convergence analysisImtiyaz Ahmad Bhat and Lakshmi Narayan Mishra Applied Mathematics and Computation, 2024, vol. 470, issue C 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. Keywords: Volterra-Urysohn integral equations; Functional integral equations; Trapezoidal method and Euler method; Gronwall inequality; Picard iterative method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000274 DOI: 10.1016/j.amc.2024.128555 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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