Solving time dependent PDEs via an improved modified extended BDF scheme

In a previous article the known MEBDF scheme had been extended to solve ODEs that arise in the method of lines solution of time dependent PDEs. In that article it was shown that MEBDF is superior to the widely used BDF approach in certain important classes of problems. In this paper, by following a different logic, we were able to improve the stability characteristics of MEBDF. Appropriate modifications to the code have also been made. Consequently, we investigate whether the current approach is better to the one previously presented. It is indeed shown that the instigated improvements have had a positive effect on both accuracy and efficiency. Numerical results are given to support this claim.