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المقاله
1 - A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methodsJournal of Linear and Topological Algebra , العدد 5 , السنة 4 , پاییز 2015In 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 m أکثرIn 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 radialbasis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it is independent of the geometry of the domain and it does not require any background interpolation or approximation cells. The error analysisof the method is provided. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method. تفاصيل المقالة -
المقاله
2 - Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau MethodJournal of Linear and Topological Algebra , العدد 2 , السنة 7 , بهار 2018In 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 tran أکثرIn 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 presented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method. تفاصيل المقالة -
المقاله
3 - Solving systems of nonlinear equations using decomposition techniqueJournal of Linear and Topological Algebra , العدد 4 , السنة 5 , تابستان 2016A 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 co أکثرA 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 singularity and ill-conditioning of the Jacobian. The order of convergence of proposed p-step iterative method is p + 1. Only one Jacobian inversion in the form of LU-factorization is required for a single iteration of the iterative method and in this way, it offers an efficient scheme. For the construction of our proposed iterative method, we used a decomposition technique that naturally provides different iterative schemes. We also computed the computational convergence order that confirms the claimed theoretical order of convergence. The developed iterative scheme is applied to large scale problems, and numerical results show that our iterative scheme is promising. تفاصيل المقالة -
المقاله
4 - The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.Journal of Linear and Topological Algebra , العدد 1 , السنة 6 , زمستان 2017In 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-Ga أکثرIn 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 and results are compared to the analytical solution and Triangular functions (TF), Delta basis functions (DFs), block-pulse functions , sinc fucntions, Adomian decomposition, computational, Haar wavelet and direct methods to demonstrate the validity and applicability of the proposed method. تفاصيل المقالة -
المقاله
5 - An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equationsJournal of Linear and Topological Algebra , العدد 2 , السنة 8 , بهار 2019In 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 p أکثرIn 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 demonstrate the behavior of the proposed method and to support the theoretical results of this paper. تفاصيل المقالة -
المقاله
6 - An efficient method for the numerical solution of functional integral equationsJournal of Linear and Topological Algebra , العدد 2 , السنة 9 , بهار 2020We 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 bee أکثرWe 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. تفاصيل المقالة