Comparative analysis of nonlinear Urysohn functional integral equations via Nyström method

Imtiyaz Ahmad Bhat, Lakshmi Narayan Mishra and Vishnu Narayan Mishra

Applied Mathematics and Computation, 2025, vol. 494, issue C

Abstract: In this sequel, the investigation of a diverse range of Urysohn type nonlinear functional integral equations falling under the Fredholm type is examined. This equation encompasses various integral and functional equations as specific instances. By imposing smoothness conditions on the involved functions, both the solution's existence and its uniqueness using the fixed point method are established. Subsequently, we employ the Nyström method for solution's approximation, leading to a set of algebraic equations of nonlinear form. The Picard iterative method is then applied to the solution's approximation for this system of algebraic equations. Additionally, the trapezoidal method is applied to approximate the solution and a novel Grönwall inequality is used to establish the convergence of method, providing a reliable theoretical foundation. Numerical examples and a comparative analysis are presented to demonstrate the convergence, effectiveness, and superiority of the Nyström method compared to the trapezoidal method, highlighting its improved practicality and versatility.

Keywords: Functional integral equations; Nyström method; Gaussian rule of quadrature; Picard iteration; Trapezoidal rule; Grönwall inequality (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000141

DOI: 10.1016/j.amc.2025.129287

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