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 nonself-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.