Hybrid method of fuzzy homotopy and runge kutta fehlberg method for solving fuzzy nonlinear equations

Abstract

The system of fuzzy nonlinear equations plays an important role in solving real-world problems. However, to solve the system of fuzzy nonlinear equations is not an easy task. This is patently obvious when dealing with trigonometric, hyperbolic, and exponential functions. Therefore, a numerical method is needed in order to overcome this issue. In this dissertation, a hybrid method of Fuzzy Homotopy and Runge Kutta Fehlberg is proposed to solve the system of fuzzy nonlinear equations. This method is extended from the Fuzzy Homotopy and Continuation Method proposed in the literature. The proposed hybrid method involves numerically finding the solution from known problems and continuing the solution until the unknown problem is found. The algorithm of the proposed hybrid method is developed and tested on a numerical example. The results are analyzed and compared with the existing methods in terms of errors, accuracy and convergence. Based on the results, the proposed hybrid method showed less error and good result in terms of accuracy and convergence compared to the existing methods. Therefore, the proposed hybrid method is superior and can be employed to solve complex system of fuzzy nonlinear equations.