Author(s)

Fatheah Ahmed Hendi¹, Manal Mohamed Al-Qarni²

¹Department of Mathematics Faculty of Science, King Abdul Aziz University, Jeddah, KSA.
²Department of Mathematics Faculty of Science, King Khaled University, Abha, KSA.

In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.

Singular Integral Equation, Linear and Nonlinear V-FIE, Adomian Decomposition Method (ADM), Carleman Kernel, Logarithmic Kernel

Hendi, F. and Al-Qarni, M. (2016) Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel. American Journal of Computational Mathematics, 6, 245-250. doi: 10.4236/ajcm.2016.63025.