Diagonalizable extended backward differentiation formulas

被引:7
作者
Frank, JE [1 ]
Van der Houwen, PJ [1 ]
机构
[1] CWI, NL-1090 GB Amsterdam, Netherlands
来源
BIT | 2000年 / 40卷 / 03期
关键词
initial-value problems; extended BDFs; parallelism;
D O I
10.1023/A:1022367713296
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
We generalize the extended backward differentiation formulas (EBDFs) introduced by Cash and by Psihoyios and Cash so that the system matrix in the modified Newton process can be block-diagonalized, enabling an efficient parallel implementation. The purpose of this paper is to justify the use of diagonalizable EBDFs on parallel computers and to offer a starting point for the development of a variable stepsize-variable order method. We construct methods which are L-stable up to order p = 6 and which have the same computational complexity per processor as the conventional BDF methods. Numerical experiments with the order 6 method show that a speedup factor of between 2 and 4 on four processors can be expected.
引用
收藏
页码:497 / 512
页数:16
相关论文
共 15 条
[1]  
[Anonymous], NUMERICAL METHODS ST
[2]   A parallel stiff ODE solver based on MIRKs [J].
Bendtsen, C .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1997, 7 (1-2) :27-36
[3]   AN MEBDF CODE FOR STIFF INITIAL-VALUE PROBLEMS [J].
CASH, JR ;
CONSIDINE, S .
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1992, 18 (02) :142-155
[5]  
Cashs JR, 1983, COMPUT MATH APPL, V5, P645
[6]  
DENK G, 1989, P C NUM TREATM DIFF
[7]  
DESWART JJB, 1997, THESIS U AMSTERDAM
[8]  
FRANK JE, 2000, IN PRESS IMA J NUMER
[9]  
FRANK JE, 1999, MASR9917 CWI
[10]  
Hairer E., 1991, SOLVING ORDINARY DIF