A-stable methods for the numerical solution of stiff initial value problems

In this paper , we present a new class of numerical methods of multistep nature that make use of second order derivatives (similar to Second Derivative Multistep Methods of Enright) and one additional stage(or off-step) point for the numerical solution of initial value problems (IVPs) for stiff ordinary differential equations (ODEs) . Stability domains of our presented methods have been obtained , showing that this class of efficient numerical methods are A) ) -stable of order up to 10 and they have wide stability regions comparing with those of some known methods like modified EBDF (MEBDF) , adaptive EBDF (A-EBDF) and Enright’s second derivative methods . Numerical results are also given for two test problems

Keywords:

Stiff ODEs , Off-step point , Hybrid method , Stability aspects