Applied Mathematics & Information Sciences

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In this paper, we establish, in a general case, the Volterra integral equation (VIE) from the initial value problems (IVPs). Also, some analytical and numerical methods are used to obtain the solution of VIE with a continuous kernel. In the numerical applications, the researcher based the Runge-Kutta and Trapezoid rules on the Simpson rule. This reference gives a fast convergence in the solution, a convergent error, and less than the previous traditional methods. Many numerical examples using Maple 18 are considered, and the estimated error, in each case, is computed. Keywords:

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