Mathematica Eterna
Open Access

Abstract

Wavelet Based Methods for Numerical Solutions of Two Dimensional Integral Equations

En-Bing Lin and Yousef Al-Jarrah

Integral equations are useful in many branches of mathematics and science as well. We begin with a brief summary of solving different kinds of one dimensional integral equations, namely, Fredholm Integral equation of the first and the second kind, Volterra integral equation of the second kind and Fredholm-Volterra integral equation as well as the discussions of singular and nonlinear integral equations. We will also discuss solving two-dimensional integral equations. There are many different methods of solving integral equations. Wavelet based methods are of particular interest. The localization property, robustness and other features of wavelets are essential to solving integral equations efficiently. We will present a wavelet based method together with several convergence results of the method. A few examples will also be presented. Some of these examples have been tested by others. We will compare the results with other methods.