Solving Two-Dimensional Fredholm Integral Equations Using Radial Basis Functions رسالة ماجستير

Abstract

As its title indicates, this study was devoted to solving Fredholm integral equation in two dimensions, using Radial Basis Functions (RBF) and RBF thin plate splines in particular. Fredholm integral equation is an import equation with many applications in science and engineering. There are different RBF bases in scholarly research. Researchers have used Gaussian and the inverse multi-quadric RBFs given their attributes when dealing with engineering appli- cations. However, new types of RBFs have been introduced with more flexible mathematical properties. In this study, we used the thin plate splines as basis functions to introduce a solution for Fredholm integral equation. After finding the analytical solution for Fredholm integral equation, we introduced a number of RBF bases to solve the integral equation using the introduced types, including the thin plate splines. Then we conducted a numerical comparison for the error between these different types, using numerical examples. we concluded with a

testing of the efficiency of existing approaches compared to this approach.