Product Block by Block for the Second Kind Volterra Integral Equations with Singular Kernel

Abstract

The block-by -block method is a good self-starting method for solving Volterra Integral equations of the second kind with continuous kernel. In this paper two modifications are suggested to develop block by block method to solve Volterra integral equations with weakly singular kernels. The idea of the product technique with higher order is used for block-by block method, which is the first modification, while the second modification is using the method on the graded nodes. Implementation and testing of the considered algorithms have been done. The results showed that this method gives good results compared with others methods on equal spaced nodes. AMS Subject Classification: 65L05, 65R20 Keywords: VOLTERRA INTEGRAL EQUATION, PRODUCT INTEGRATION, SINGULAR KERNEL, BLOCK -BY-BLOCK METHOD, BOOL’S QUADRATURE.