Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule - A. Asanov; S. Yanık (MANAS: Journal of Engineering)
In this paper, the generalized Simpson's rule (GSR) is applied to solve linear Fredholm-Stieltjes integral equations of the second kind (LFSIESK). A numerical example is presented to illustrate the method by using Maple. In some cases depending on the number of subintervals “n” , the results are calculated and compared. The graph of these results is plotted. An algorithm of this application is given by using Maple. The theory of integral equation with its applications plays an important role in applied mathematics. Integral equations are used as mathematical models for many and varied physical situations and they also occur as reformulations of other mathematical problems [7]. For many integral equations, it is necessary to use approximation methods. As an example, most of the geophysical problems connected with electromagnetic and seismic wave propagation can only be solved approximately. Among theintegral equations, linear Fredholm integral equations of second kind is one of the most popular types of integral equations [7] [13]. Many approximation methods can be used to solve linear Fredholm integral equations of second kind. However, only a few of them are useful to solve LFSIESK. The generalized Simpson's rule is one of the most suitable method with its pretty close result to solve LFSIESK.