The extended backward differentiation formulas (EBDFs) and their modified form (MEBDF) were proposed by Cash in the 1980s for solving initial-value problems (IVPs) for stiff systems of ordinary differential equations (ODEs). In a recent performance evaluation of various IVP solvers, including a variable-step-variable-order implementation of the MEBDF method by Cash, it turned out that the MEBDF...

K e y w o r d s M E B D F , Large sparse systems of stiff IVPs and differential-algebraic equations, Time dependent PDEs. 1 . I N T R O D U C T I O N In th i s pape r , we will be concerned wi th the numer ica l so lu t ion of the in i t ia l value p rob l e m dy M~x = f (x ,y) , y(xo) = Yo. (1.1) We will be p a r t i c u l a r l y concerned wi th two i m p o r t a n t cases. (i) M = I and so w...

Department of Mathematics, Faculty of science, Razi university, Kermanshah 67149, Iran. Abstract In this paper, we present a new method for solving of the Burger’s equation by combination of method of lines (MOL) and matrix free modified extended backward differential formula (MF-MEBDF). The method of lines semi discretization approach is used to transform the model partial differential equatio...

Hessenberg differential algebraic equations (Hessenberg-DAEs) with a high index play critical role in the modeling of mechanical systems and multibody dynamics. Motivated by widely used Lie-group equation (LGDAE) method, which handles index-2 systems, we first propose modified extended (MELGDAE) method for solving index-3 Hessenberg-DAEs then provide theoretical analysis to deepen foundation ME...