Abstract—In this paper, the efficient methods based on the Sinc approximation with the single exponential (SE) and double exponential (DE) transformations are presented to solve nonlinear Fredholm-Volterra integral equations with weakly singular kernel. Sinc approximation has considerable advantages. Some of them are the exponential convergence of an approximate solution and simply implementation, even in the presence of singularities. Properties of the SE-Sinc and DE-Sinc methods are utilized to reduce the problem to a set of algebraic equations. Finally, we give some numerical results that confirm efficiency and accuracy of the numerical schemes.

Index Terms—Nonlinear Fredholm-Volterra integral equation, Sinc approximation, weakly singular kernel.

The authors are with School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran (email: maleknejad@iust.ac.ir).

Cite: Khosrow Maleknejad, Azadeh Ostadi, Asyieh Ebrahimzadeh, "Numerical Solution of Nonlinear Weakly Singular Fredholm-Volterra Integral Equations of the Second Kind by Using Sinc-Collocation Methods," International Journal of Applied Physics and Mathematics vol. 6, no. 3, pp. 88-94, 2016.