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:
Digital Object Identifier (DOI)
A. Elsayed, M.
"Some Different Methods via the Solution of Volterra Integral Equation,"
Applied Mathematics & Information Sciences: Vol. 16:
6, Article 14.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss6/14