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.