Abstract
In this study, the second kind Volterra integral equations (VIEs) are considered. An algorithm based on the two-point Taylor formula as a special case of the Hermite interpolation is proposed to approximate the solution of such problems. The method can be applied for solving both the linear and nonlinear VIEs and systems of nonlinear VIEs. The convergence analysis and the error estimate of the method are described. A multistep form of the algorithm which is particularly beneficial in large intervals is also presented. The main advantage of the proposed algorithm is that it gives high accurate results in acceptable computational times. In order to indicate the validity of the method, it is employed for solving several illustrative examples. The efficiency of the method is confirmed through our study respecting the absolute errors and CPU times.
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