Heterogeneous multiscale methods for stiff ordinary differential equations

被引:115
作者
Engquist, B [1 ]
Tsai, YH
机构
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] Princeton Univ, PACM, Princeton, NJ 08544 USA
[3] Royal Inst Technol KTH, SE-10044 Stockholm, Sweden
[4] Princeton Univ, Inst Adv Study, Princeton, NJ 08544 USA
关键词
D O I
10.1090/S0025-5718-05-01745-X
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing different time scales. Stability and convergence results for the proposed HMM methods are presented together with numerical tests. The analysis covers some existing methods and the new algorithms that are based on higher-order estimates of the effective force by kernels satisfying certain moment conditions and regularity properties. These new methods have superior computational complexity compared to traditional methods for stiff problems with oscillatory solutions.
引用
收藏
页码:1707 / 1742
页数:36
相关论文
共 36 条
[1]  
Arnold V., 1989, MATH METHODS CLASSIC, DOI DOI 10.1007/978-1-4757-2063-1
[2]  
Bogoliubov N.N., 1961, International Monographs on Advanced Mathematics and Physics
[3]  
BROWNING GL, 1994, MON WEATHER REV, V122, P2614, DOI 10.1175/1520-0493(1994)122<2614:SMFPWD>2.0.CO
[4]  
2
[5]   STABILITY OF 2-STEP METHODS FOR VARIABLE INTEGRATION STEPS [J].
DAHLQUIST, GG ;
LINIGER, W ;
NEVANLINNA, O .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (05) :1071-1085
[6]  
ENGQUIST B, 2005, LECT NOTES COMPUTATI, V44
[7]   Long-time-step methods for oscillatory differential equations [J].
Garcia-Archilla, B ;
Sanz-Serna, JM ;
Skeel, RD .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 20 (03) :930-963
[8]   MULTIRATE LINEAR MULTISTEP METHODS [J].
GEAR, CW ;
WELLS, DR .
BIT, 1984, 24 (04) :484-502
[9]  
GEAR CW, 2002, COARSE INTEGRATION B
[10]   MODIFIED MULTIREVOLUTION INTEGRATION METHODS FOR SATELLITE ORBIT COMPUTATION [J].
GRAF, OF ;
BETTIS, DG .
CELESTIAL MECHANICS, 1975, 11 (04) :433-448