A comparative study on HBDF based methods for the numerical solutions of stiff systems

For the numerical solutions of stiff systems of ODEs and PDEs, there are so many multistep methods based on BDF methods. In recent yesrs, hybrid methods based on BDFs are introduced in order to improve stability regions and required high orders. In this paper, we are going to introduce a new class of high order HBDF based methods (of order p; p = 2; 3; ...; 12) with wide stability regions compared to those of A-EBDF and MEBDF methods. Numerical results of two test examples show that new methods have also very good performance in saving CPU time due to number of function evaluations and presented back substitutions per time step.