Search

In this manuscript, a new class of high-order multistep methods on the basis of hybrid backward differentiation formulas (BDF) have been illustrated for the numerical solutions of systems of ordinary differential equations (ODEs) arising from semi-discretization of time dependent partial differential equations. Order and stability analysis of the methods have been discussed in detail. By using an off-step point together with a step point in the first derivative of the solution, the new methods obtained are A-stable for order p, (p = 4 , 5 , 6 , 7) and A (α )-stable for order p, (p = 8 , 9 , ... , 14). Compared to the existing BDF based method, i.e. class 2 + 1 , hybrid BDF methods (HBDF), super-future points based methods (SFPBM) and MEBDF, there is a good improvement regarding to absolute stability regions and orders. Some numerical examples are given in order to check the advantage of these methods in reducing the CPU time and thus in increasing accuracy of low and high order the new methods compared to those of SFPBM and MEBDF. [ABSTRACT FROM AUTHOR]

In this article, the details of new hybrid methods have been presented to solve systems of ordinary differential equations (ODEs). These methods are based on backward differentiation formulae (BDF) where one additional stage point (or off-step point) and two step points have been used in the first derivative of the solution to improve the absolute stability regions compared with some existing methods such as BDF, extended BDF (EBDF) and modified EBDF (MEBDF). Stability domains of our new methods have been obtained showing that these methods, we say Class 2+1 Hybrid BDF-Like methods, are A-stable for order p, p=3,4, and A( α)-stable for order p, p=5, 6, 7, 8. Numerical results are also given for five test problems. [ABSTRACT FROM AUTHOR]