Numerical Techniques for Solving Integral Equations with Carleman Kernel

Abstract

Integral equations with Carleman type kernel arise frequently in physics and engineering,theory of elasticity, mathematical problems of radiativeheat transformationsand radiative equilibrium. In this work we focus our attention mainly on the numerical handling of the Fredholm and Volterra integral equations with Carleman kernel. The numerical treatment of such equations can be achieved by using the following numerical techniques, namely; Toeplitz matrix method, Product Nystrom method, sinc-collocation method and Laplace Adomian decomposition method. To test the efficiency of these methods, we consider some numerical test cases. Numerical results have shown that product Nystrom method is one of the most powerful numerical techniques for solving Fredholm integral equation with a Carleman kernel in comparison with the other numerical techniques. On the other hand, we see clearly that the Laplace Adomian decomposition method is a very reliable and efficient method for solving Volterra integral equations with Carleman kernel.