Computational Analysis of Two-parameter Integro-differential Problems in LCR-circuits

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.