THE NUMERICAL SOLVABILITY OF WEAKLY SINGULAR INTEGRAL ALGEBRAIC EQUATIONS OF INDEX-1

In this paper, we study the polynomial collocation method applied to a particular class of Integral Algebraic Equations (IAEs) with weakly singular kernels. An ultraspherical collocation method including the matrix-vector multiplication representation of solution is proposed for the semi explicit IAEs of index-1. Some function transformations are also used to transform the system into an equivalent IAEs system, so that the solution of the altered equation possesses better regularity. Some numerical results are also given to illustrate the efficiency of the method.