A New Method for Solving Multi-Dimensional Fredholm Integral Equations and Its Convergence Analysis
Subject Areas : International Journal of Industrial Mathematics
1 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Keywords: Multi-dimensional linear and nonlinear, Fredholm Integral Equations, Multi-dimensional expansion, Convergence analysis, Boundary conditions,
Abstract :
In this paper, we focus on obtaining an approximate solution for multi-dimensional Fredholm integral equations of second kind. An expansion method is used for treatment multi-dimensional Fredholm integral equation of second kind. This method reduces multi-dimensional integral equation to a partial differential equation. After constructing boundary conditions, this partial differential equation reduces to algebraic equation that can be solved easily with any of the usual methods. Furthermore some theorems are proved for convergence analysis. Finally, for showing the efficiency of the method we use some numerical examples
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