Hybridization of the shooting and Runge-Kutta Cash-Karp methods for solving Fuzzy Boundary Value Problems

Abstract

Fuzzy Differential Equations (FDEs) have attracted great interest among researchers. These FDEs have been used to develop a mathematical model for everyday life problems. In this study, we propose a solution method for a second-order Fuzzy Boundary Value Problem (FBVP). Four systems of FBVPs were developed based on the generalized fuzzy derivative. The second-order FBVP for each system was divided into two parts: Fuzzy non-homogeneous and fuzzy homogeneous equations. Using the shooting method, these two equations were then reduced to first-order FDEs. By implementing the Fuzzy Runge-Kutta Cash-Karp of the fourth-order method (FRKCK4), the approximate solution was compared with the analytical solution and the solution from the Fuzzy Runge-Kutta of the fourth-order method (FRK4).

Keywords

• fuzzy boundary value problem
• runge-kutta cash-karp
• fuzzy differential equations