M. Nili Ahmadabadi
Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
[ 1 ] - Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
In this paper, a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method. In this method, a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution. Error analysis of this method is also ...
[ 2 ] - The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...
[ 3 ] - Solving systems of nonlinear equations using decomposition technique
A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...
[ 4 ] - A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods
In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...
[ 5 ] - An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations
In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions. Finally, some numerical examples are given to demons...
[ 6 ] - An efficient method for the numerical solution of functional integral equations
We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained.
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