This article essays the numerical solution of singularly perturbed Volterra integro-differential equations using some finite difference techniques. At first, the upwind scheme is applied for the derivative component and for the integral component, the trapezoidal rule in conjunction with the right side rectangular rule is used. This approach achieves first order uniform convergence. Furthermore, Richardson extrapolation is implemented to improve the accuracy by accelerating up the rate of convergence of the upwind scheme to obtain a second order accuracy. Finally, a hybrid scheme is applied, wherein central difference scheme is applied on the finer mesh region and midpoint difference operator on the coarser mesh region. The hybrid scheme also provides a second order uniform convergence. Numerical experiments are done with test problems and comparison is drawn with the existing methods to show the robustness of the proposed schemes.
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Panda, A., Mohapatra, J. & Reddy, N.R. A Comparative Study on the Numerical Solution for Singularly Perturbed Volterra Integro-Differential Equations. Comput Math Model 32, 364–375 (2021). https://doi.org/10.1007/s10598-021-09536-9
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DOI: https://doi.org/10.1007/s10598-021-09536-9