The Integration of Stiff Systems of ODEs Using NDFs and MEBDFs

Abstract

In this paper we modify the MEBDF method using the NDFs as predictors instead of the BDFs. We have done it in three different ways: changing both predictors of the MEBDF, changing only the first predictor and changing only the second one. We have called the new methods MENDF, MENBDF and MEBNDF respectively. The new methods are A-stable up to order $4$ and the stability properties of the new methods are better than the MEBDF method.