Quarter-Sweep Iterative Methods for Fuzzy Fredholm Integral Equations of the Second Kind

Abstract

This study presents a numerical solution of fuzzy Fredholm integral equations (FIEs) using the quarter-sweep Jacobi (QSJ) and Gauss-Seidel (QSGS) iterative methods. The primary goal is to apply the quarter-sweep concept in the discretisation process to reduce computational complexity in solving such equations. The methodology of this study consists of two main parts. First, we implement a quadrature scheme that incorporates with quarter-sweep concept to discretise the fuzzy FIEs, resulting in corresponding linear equations. This approach then generates a system of linear equations with respect to the proposed problem. Subsequently, QSJ and QSGS method are utilised to address the resulting system of linear equations. To demonstrate the effectiveness of this approach, several examples are tested. The results obtained highlight the effectiveness of proposed methods in addressing fuzzy FIEs.