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

Sharefa EISA ALI ALHAZMI

Abstract: 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.

Keywords: Abel, logarithm kernel, Block-Pulse Function, Taylor expansion, Error analysis

How to Cite?: Sharefa EISA ALI ALHAZMI, "A Computational Approach for Solving Singular Volterra Integral Equations with Abel Kernel and Logarithmic Singularities Using Block Pulse Functions", Volume 4 Issue 1, January 2015, International Journal of Science and Research (IJSR), Pages: 538-548, https://www.ijsr.net/getabstract.php?paperid=SUB14942, DOI: https://dx.doi.org/10.21275/SUB14942