Solving First-Order Nonlinear Fuzzy Initial Value Problems Using Two-Step Block Method with Presence of Higher Derivatives

Abstract

Fuzzy differential equation models are suitable where uncertainty exists for real-world phenomena. Numerical techniques are used to provide an approximate solution to these models in the absence of an exact solution. However, existing studies that have developed numerical techniques for solving FIVPs possess an absolute error accuracy that could be improved. This is as a result of the low order and non-self-starting properties of the developed numerical techniques by previous studies. For this reason, this study, develops an Obrechkoff-type two-step implicit block method with the presence of second and third derivative for the numerical solution of first-order nonlinear fuzzy initial value problems. The convergence properties for the proposed block method are described in detail. Then the proposed method is adopted to solve first-order nonlinear fuzzy initial value problems with triangular and trapezoidal fuzzy numbers. The obtained results indicates that the proposed method effectively solves first-order nonlinear fuzzy initial value problems with better accuracy.