TITLE:
Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel
AUTHORS:
Fatheah Ahmed Hendi, Manal Mohamed Al-Qarni
KEYWORDS:
Singular Integral Equation, Linear and Nonlinear V-FIE, Adomian Decomposition Method (ADM), Carleman Kernel, Logarithmic Kernel
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.3,
September
14,
2016
ABSTRACT: 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.