Matrix free MEBDF method for the solution of stiff systems of ODEs

In this paper, we present the details of a new method which is a hybrid method of MF-BDF and MEBDF. To obtain this new method which we call MF-MEBDF, we compose the matrix free properties of the first method and the accuracy of MEBDF, elaborately. Application of this new method to some important stiff problems show that MF-MEBDF is generally faster than MEBDF and more accurate than MF-BDF and MEBDF. Since in MEBDF, the LU factorization is used, we expect MF-MEBDF to be more efficient than the other two methods for large stiff systems of ODEs.