AGE Iterative Method with First-Order Quadrature Scheme for Fuzzy Fredholm Integral Equations of Second Kind

Abstract

Abstract In this study, we propose Alternating Group Explicit (AGE) iterative method to solve the problem of linear fuzzy Fredholm integral equations of the second kind (FFIE-2) based on Trapezoidal quadrature rule. First, we generate a system of linear equations by using approximation equations. Next, we use AGE iterative method to solve the generated linear system of FFIE-2. Then, we illustrate the applicability of AGE iterative method on some numerical examples. Finally, we do the comparison to test the efficiency of AGE with Jacobi and Gauss-Seidel (GS) iterative method based on three parameters: number of iterations, execution time and Hausdorff distance. From our findings, we found that AGE is a better iterative method compared with Jacobi and GS to solve FFIE-2.