Efficient parallel multivalue hybrid methods for stiff differential equations

A class of efficient parallel multivalue hybrid methods for stiff differential equations are presented, which are all extremely stable at infinity,A-stable for orders 1–3 and A(α)-stable for orders 4–8. Each method of the class can be performed parallelly using two processors with each processor having almost the same computational amount per integration step as a backward differentiation formula (BDF) of the same order with the same stepsize performed in serial, whereas the former has not only much better stability properties but also a computational accuracy higher than the corresponding BDF. Theoretical analysis and numerical experiments show that the methods constructed in this paper are superior in many respects not only to BDFs but also to some other commonly used methods.