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Numerical Treatment of Nonlinear Volterra-Fredholm Integral Equation with a Generalized Singular Kernel
Department of Mathematics Faculty of Science, King Abdul Aziz University, Jeddah, KSA
Department of Mathematics Faculty of Science, King Khaled University, Abha, KSA
- 1 Department of Mathematics Faculty of Science, King Abdul Aziz University, Jeddah, KSA
- 2 Department of Mathematics Faculty of Science, King Khaled University, Abha, KSA
American Journal of Computational Mathematics·Volume 06 (2016)·Pages 245–250·Published 4 July 2016·DOI10.4236/ajcm.2016.63025
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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.
KeywordsSingular Integral EquationLinear and Nonlinear V-FIEAdomian Decomposition Method (ADM)Carleman KernelLogarithmic Kernel
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