Work

Richardson Extrapolation for Singularly Perturbed Fredholm Integro Differential Equations

Year: 2025

Type: article

Abstract: This study numerically derived the higher order convergence for a class of singularly perturbed Fredholm integro differential equations with reaction diffusion and convection diffusion type problems. A non-standard finite difference approach is used to approximate the derivatives. The trapezoidal rule determines the integral term. The suggested numerical technique achieves a uniform convergence rate independently of the perturbation parameter. Implementing the Richardson extrapolation technique achieves a fourth order convergence rate for reaction diffusion type problems and a second order convergence rate for convection diffusion type problems. Specific numerical examples are provided to corroborate in practice the effectiveness of the theoretical findings.

Source: International Journal of Mathematical Engineering and Management Sciences

DOI: 10.33889/ijmems.2025.10.6.094

Authors: P. Antony Prince, L. Govindarao, Sekar Elango

Institution: Amrita Vishwa Vidyapeetham

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $500

Funder: Amrita Vishwa Vidyapeetham University