P. Antony Prince
Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, Tamil Nadu, India.

L. Govindarao
Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, Tamil Nadu, India.

Sekar Elango
Department of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, Tamil Nadu, India.

DOI https://doi.org/10.33889/IJMEMS.2025.10.6.094

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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.

Keywords- Singular perturbation, Extrapolation, Fitted operator, Fredholm integral, Boundary layer.

Citation

Prince, P. A. Govindarao, L., & Elango, S. (2025). Richardson Extrapolation for Singularly Perturbed Fredholm Integro Differential Equations. International Journal of Mathematical, Engineering and Management Sciences, 10(6), 2023-2039. https://doi.org/10.33889/IJMEMS.2025.10.6.094.