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Abstract This thesis is concerned with the numerical solution of integral equations of the second kind volterra from. Volterra integral equations are essentially” initial value” problems for ordinary differential equations. In reality any of such problems can be reformulated as as a volterra equations. Examples of these include problems of apreferential direction (e.g. time, energy, etc.) methods of solution of volterra integral equation can be classified into two categories ; analytical solutions and numerical solutions. Analytical solutions include methods such as differentiation, laplace transformation and resolvent kerel. But these methods solve volterra integral equations whose kernel k(x, t) is dependent solely on the difference (x-t). so complicated from of the kernel will complicate the analytical method used. In practical applications, it is almost invariably necessary to solve the integral equations numerically. |