الفهرس 
Introduction
The quadrature methodsOnly 14 pages are availabe for public view
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Abstract
According to wide spread application of Volterra integral equations in many engineering fields, searching for solutions are to be subject to many researchers. Analytical methods play its role in solving linear integral equations, and according to complexity in finding analytical solution to all nonlinear and weakly singular integral equations, so urgent need to use numerical methods with some developments to carry out higher accuracy. This research handles a study about Volterra integral equations of the second kind, linear and nonlinear equations, and weakly singular type, in addition to demonstrate some methods used in numerical solution. The most famous methods used in numerical solution to solve linear and nonlinear integral equations are the Quadrature and Projection methods, and the more important Projection method is the Collocation one. The used methods to solve weakly singular integral equations are Product Integration and Collocation methods. The research contains also an introduction to Fractional calculus, and the connection of fractional differential equations with weakly singular Volterra integral equations (Linear and nonlinear). Some developments are performed to the Product Integration method; these developments are contributing to improvement of the accuracy of results. Also we find complete forms to weights used in approximating the solution of weakly singular Volterra integral equations by the Collocation method. from the comparison to all previous methods, it is appears that as the degree of polynomial used to approximate the integration form leads to improvement of the accuracy of results. Briefly it is clear that the Collocation method is the best used method, which gives higher order of converge