Exponentially-fitted Runge-Kutta Method for Volterra Integro-Differential Equations
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Abstract
The present paper is intended to construct the exponentially fitted Runge-Kutta method to solve Volterra integro-differential equation (VIDE). Here, VIDE is first converted into its equivalent integro-differential operator form and assumes that these operators annihilate the pre-assigned set functions with unknown frequencies and . The optimum values of these frequencies and are calculated by minimizing the truncation error. To show the utility of the proposed development, these schemes are tested on two examples of VIDE having exponential solution. The comparison of the numerical results with the analytical/exact solution and the best-reported results in literature confirms the high accuracy and applicability of the proposed method to the VIDE.
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