A numerical technique for solving nonlinear singularly perturbed Fredholm integro-differential equations

Abhilipsa Panda, Jugal Mohapatra, Ilhame Amirali, Muhammet Enes Durmaz and Gabil M. Amiraliyev

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 618-629

Abstract: This study deals with two numerical schemes for solving a class of singularly perturbed nonlinear Fredholm integro-differential equations. The nonlinear terms are linearized using the quasi-linearization technique. On the layer adapted Shishkin mesh, the numerical solution is initially calculated using the finite difference scheme for the differential part and quadrature rule for the integral part. The method proves to be first-order convergent in the discrete maximum norm. Then, using a post-processing technique we significantly enhance the accuracy from first order to second order. Further, a hybrid scheme on the nonuniform mesh is also constructed and analyzed whose solution converges uniformly, independent of the perturbation parameter and directly gives second order accuracy. Parameter uniform error estimates are demonstrated and the theoretical results are validated through some numerical tests.

Keywords: Fredholm integro-differential equation; Singular perturbation; Hybrid scheme; Richardson extrapolation; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:618-629

DOI: 10.1016/j.matcom.2024.02.011

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