Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)ý. ýThe solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations systemý. ýIn this articleý, ýthe obtained nonlinear system has been solved as a dynamical systemý. ýThe solution of the obtained nonlinear system by the dynamical system through the Newton numerical method has got a particular priorityý, ýin thatý, ýin this methodý, ýthe number of the unknowns could be more than the number of equationsý. ýBesidesý, ýthe point of departure of the system could be an infeasible pointý. ýIt has been proved that the obtained dynamical system is stableý, ýand the response of this system can be achieved by using of the fourth order Runge-Kuttaý. ýThe results of this method is comparable with the similar numerical methods; in most of the casesý, ýthe obtained results by the presented method are more efficient than those obtained by other numerical methodsý. ýThe efficiency of the new method will be investigated through examples.