Application of the 2-Step Reverse Differentiation Formula Method (BDF2) in Initial Value Problems

Abstract

In this text, the results of the PVI resolution studies using the prediction-correction method are presented. For prediction, the explicit method of Adams-Bashforth was used and for correction, the implicit method of Adams-Moulton. The Retrograde Differentiation method in two long methods (BDF2) is used to solve a prediction correction problem with two lower-order methods of using a predictor and a verification method in the same way in the correct step and checking the order of BDF2 correction formula is zero-stable. The study of the BDF2 method to solve an implicit scheme requires, as a prerequisite, the Linear Steps or Multiple Linear Steps Methods (MLSMs), the Local Truncation Error (LTE) - to verify the consistency, and the characteristic polynomial to verify if the method is zero-stable.