Integral equations
1. An efficient method for the numerical solution of functional integral equations

M. Nili Ahmadabadi

Volume 09, Issue 02 , Spring 2020, , Pages 105-111

Abstract
  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.  Read More

Linear and multilinear algebra; matrix theory
2. An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations

A‎. ‎M‎. ‎E‎. ‎ Bayoumi; M. A. Ramadan; M. Nili Ahmadabadi

Volume 08, Issue 02 , Spring 2019, , Pages 117-126

Abstract
  ‎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 ...  Read More

Integral equations
3. Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

H. Laeli Dastjerdi; M. Nili Ahmadabadi

Volume 07, Issue 02 , Spring 2018, , Pages 75-85

Abstract
  ‎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 ...  Read More

Difference and functional equations
4. The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.

J. Nazari; M. Nili Ahmadabadi; H. Almasieh

Volume 06, Issue 01 , Winter 2017, , Pages 11-28

Abstract
  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. ...  Read More

Difference and functional equations
5. Solving systems of nonlinear equations using decomposition technique

M. Nili Ahmadabadi; F. Ahmad; G. Yuan; X. Li

Volume 05, Issue 03 , Summer 2016, , Pages 187-198

Abstract
  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 ...  Read More

Integral equations
6. A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods

M. Nili Ahmadabadi; H. Laeli Dastjerdi

Volume 04, Issue 04 , Autumn 2015, , Pages 289-304

Abstract
  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 ...  Read More