On the numerical solution of integral equations of the fourth kind with higher index: differentiability and tractability index-3

Abstract

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and di fferentiability index of the given system are 3. Tractability and di erentiability index are introduced based on the -smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give su cient conditions for the existence and uniqueness of the solutions for the index-3 system. Then, a numerical technique based on the Chebyshev polynomial collocation methods including the matrix-vector multiplication representation is proposed for the solution of these systems and the performance of the numerical scheme is illustrated by means of some test problems.