A Runge-Kutta method with reduced number of function evaluations to solve hybrid fuzzy differential equations

作者：Ahmadian Ali^*; Salahshour Soheil; Chan Chee Seng

来源：Soft Computing, 2015, 19(4): 1051-1062.

DOI：10.1007/s00500-014-1314-9

• Fuzzy ordinary differential equation
• Hybrid system
• Bede's characterization theorem
• High order Runge-Kutta method
• Seikkala derivative

In this paper, we employ a numerical algorithm to solve first-order hybrid fuzzy differential equation (HFDE) based on the high order Runge-Kutta method. It is assumed that the user will evaluate both and readily, instead of the evaluations of only when solving the HFDE. We present a method that requires only three evaluations of . Moreover, we consider the characterization theorem of Bede to solve the HFDE numerically. The convergence of the method will be proven and numerical examples are shown with a comparison to the conventional solutions.

• 出版日期2015-4