Legendre–Gauss–Lobatto collocation method for solving multi-dimensional Fredholm integral equations - Bhrawy, A.H. (2016)
This paper reports a new spectral collocation technique for solving second kind Fredholm integral equations (FIEs). We develop a collocation scheme to approximate FIEs by means of the shifted Legendre–Gauss–Lobatto collocation (SL–GL-C) method. Moreover, we adapt the SL–GL-C algorithm to solve one dimensional second kind FIEs and system of FIEs. Two numerical algorithms are also investigated to solve the two dimensional FIEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.