%0 Journal Article
%T Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems
%J Control and Optimization in Applied Mathematics
%I Payame Noor University (PNU)
%Z 2383-3130
%A Soleymanpour Bakefayat, Azhdar
%A Karamseraji, Sima
%D 2017
%\ 04/01/2017
%V 2
%N 1
%P 43-63
%! Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems
%K Second kind Fredholm-Volterra integral equations
%K Nonlinear systems
%K Dynamical systems
%K Triangular functions
%K Block-pulse functions
%R
%X The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp). The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system. In this article, the obtained nonlinear system has been solved as a dynamical system. The solution of the obtained nonlinear system by the dynamical system through the Newton numerical method has got a particular priority, in that, in this method, the number of the unknowns could be more than the number of equations. Besides, the point of departure of the system could be an infeasible point. It has been proved that the obtained dynamical system is stable, and the response of this system can be achieved by using of the fourth order Runge-Kutta. The results of this method is comparable with the similar numerical methods; in most of the cases, the obtained results by the presented method are more efficient than those obtained by other numerical methods. The efficiency of the new method will be investigated through examples.
%U https://mathco.journals.pnu.ac.ir/article_4822_e8a61ae5105640197527a9613b607267.pdf