ABSTRACT
In [1] the known MEBDF scheme had been used to solve ordinary differential equations (ODEs) that arise in the method of lines solution of time dependent partial differential equations (PDEs). There, it was shown that MEBDF is superior to the widely used BDF approach in certain important classes of problems. This short paper serves as an introduction to the different logic we have followed in order to improve the stability characteristics of MEBDF. Here wee are also briefly referring to the fact that our new and enhanced approach produced a marked positive effect on both the accuracy and efficiency compared to [1]. Due to space limitations we are unable to present the numerical results that support our claims.
