The Extended Block Predictor-Block Corrector Method for Computing Fuzzy Differential Equations

Abstract

Over the years, scholars have developed predictor-corrector method to provide estimates for ordinary differential equations (ODEs). Predictor-corrector methods have been reduced to predicting-correcting method with no concern for finding the convergence-criteria for each loop with no suitable vary step size in order to maximize error. This study aim to consider computing fuzzy differential equations employing the extended block predictor-block corrector method (EBP-BCM). The method of interpolation and collocation combined with multinomial power series as the basis function approximation will used. The principal local truncation errors of the block predictor-block corrector method will be utilized to bring forth the convergence criteria to ensure speedy convergence of each iteration thereby maximizing error(s). Thus, these findings will reveal the ability of this technique to speed up the rate of convergence as a result of variegating the step size and to ensure error control. Some examples will solve to showcase the efficiency and accuracy of this technique.