A Computational Approach for Solving Singular Volterra Integral Equations with Abel Kernel and Logarithmic Singularities Using Block Pulse Functions

In this paper, a computational approach for solving singular Volterra integral equations with Abel kernel or logarithmic singularities will introduced. The technique of block-pulse functions will be used to solve the linear Volterra Integral equations with Abel kernel and Logarithm Kernels. This method is based on approximating of unknown function in terms of Block Pulse Functions and Taylor series expansion of singular part. The error analysis is presented to show the efficiency. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method in solving such types of systems of Abel or Logarithm integral equations.