P. Antony Prince
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.

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

DOI https://doi.org/10.33889/IJMEMS.2026.11.2.038

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Abstract

This paper solves the two-parameter singularly perturbed Fredholm integro-differential equations through the developed exponentially fitted operator method and monotone finite difference method. The differential component is determined computationally using a developed exponentially fitted operator approach and a monotone finite difference method. The composite trapezoidal rule evaluates the integral component on a uniform grid. The developed exponentially fitted operator method gives first-order convergence when the small parameter related to the perturbation is much smaller than the square of the second parameter, and second-order convergence when the square of the second parameter is much smaller than the perturbation parameter. In addition, the monotone finite difference method shows second-order convergence in both situations. Numerical results are included to support the theoretical findings of the proposed methods.

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

Citation

Prince, P. A., Elango, S., & Govindarao, L. (2026). Computational Analysis of Two-parameter Integro-differential Problems in LCR-circuits. International Journal of Mathematical, Engineering and Management Sciences, 11(2), 920-939. https://doi.org/10.33889/IJMEMS.2026.11.2.038.