FORMULATION OF 𝒌 −STEP ORDER 𝟐𝒌 FUZZY-STRUCTURED BLOCK HYBRID BACKWARD DIFFERENTIATION FORMULAE ALGORITHMS FOR THE APPROXIMATE SOLUTION OF FUZZY DIFFERENTIAL EQUATION

Abstract

In this paper, a 𝑘 −step (𝑘 = 2,3,4), order 2𝑘 Fuzzy-structured block hybrid backward differentiation formulae were formulated for the approximate solution of fuzzy differential equations (FDE’s). 𝑘 off step points were incorporated at interpolation in the process of formulation. The methods were developed using interpolation and collocation techniques. Convergence of the methods were analyzed and established. The methods were found to be of uniform order 2𝑘 . The methods were implemented as a block method, combining the main method with some additional methods obtained from the same continuous form. Numerical experiments were carried out and the results obtained were found to be effective, efficient and accurate in comparison with the exact solutions and approximations obtained with existing methods