Efficient parallel multivalue hybrid methods for stiff differential equations  

作　　者：李寿佛 

出　　处：《Science China Mathematics》2002年第10期1276-1290,共15页中国科学：数学（英文版）

基　　金：This work was supported by the National High-Tech ICF Committee in China and the National Natural Science Foundation of China (Grant No. 19871070).

摘　　要：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. Eachmethod of the class can be performed parallelly using two processors with each processor having almost thesame computational amount per integration step as a backward differentiation formula (BDF) of the same orderwith the same stepsize performed in serial, whereas the former has not only much better stability propertiesbut also a computational accuracy higher than the corresponding BDF. Theoretical analysis and numericalexperiments show that the methods constructed in this paper are superior in many respects not only to BDFsbut also to some other commonly used methods.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.

关 键 词：STIFF DIFFERENTIAL equations  GENERAL multivalue methods  PARALLEL computation. 

分 类 号：O175[理学—数学]