Approximate solutions of nonlinear functional Volterra integral equations using ramp basis functions

Peyman Abolghasemi Qarehbolagh and Sohrab Bazm

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 727-745

Abstract: A collocation method based on ramp basis functions is proposed for the numerical solution of nonlinear functional Volterra integral equations of Urysohn type. Exploiting the local support of the ramp functions, the resulting collocation system has a lower-triangular structure, which allows the approximate solution to be computed sequentially and avoids the solution of large nonlinear algebraic systems. A convergence analysis is presented, and error estimates are derived under mild regularity assumptions using a nonlinear Gronwall inequality, which guarantee first-order convergence of the method.

Keywords: Functional integral equations; Nonlinear Volterra integral equations; Ramp functions; Collocation method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:727-745

DOI: 10.1016/j.matcom.2026.05.002

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