A NEW NUMERICAL-METHOD FOR THE INTEGRATION OF HIGHLY OSCILLATORY 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATIONS

被引：25
作者：
DENK, G
机构：
[1] Technische Universität München, Mathematisches Institut
来源：
APPLIED NUMERICAL MATHEMATICS | 1993年 / 13卷 / 1-3期
关键词：
ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATORY SOLUTIONS; MULTISTEP METHOD; CONSISTENCY; CONVERGENCE; ABSOLUTE STABILITY;
D O I：
10.1016/0168-9274(93)90131-A
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents a new discretization scheme for the efficient integration of highly oscillatory second-order ordinary differential equations. The discretization scheme is based on the principle of coherence proposed by Hersch. The analysis of the formulas reveals properties such as absolute stability and P-stability which indicate the ability of the method to handle highly oscillatory_differential equations. This is confirmed by numerical results.
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页码：57 / 67
页数：11
相关论文
共 17 条
[11]  
LAMBERT JD, 1979, COMPUTATIONAL METHOD
[12]   NUMEROV-TYPE METHODS WITH MINIMAL PHASE-LAG FOR THE NUMERICAL-INTEGRATION OF THE ONE-DIMENSIONAL SCHRODINGER-EQUATION [J].
SIMOS, TE ;
RAPTIS, AD .
COMPUTING, 1990, 45 (02) :175-181
[13]   STABILIZATION OF COWELLS METHOD [J].
STIEFEL, E ;
BETTIS, DG .
NUMERISCHE MATHEMATIK, 1969, 13 (02) :154-&
[14]  
Stoer J., 1993, INTRO NUMERICAL ANAL
[15]  
VANDENBERGHE G, 1990, INT J COMPUT MATH, V32, P233
[16]   DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTROM METHODS FOR OSCILLATORY PROBLEMS [J].
VANDERHOUWEN, PJ ;
SOMMEIJER, BP .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1989, 26 (02) :414-429
[17]   EXPLICIT RUNGE-KUTTA (-NYSTROM) METHODS WITH REDUCED PHASE ERRORS FOR COMPUTING OSCILLATING SOLUTIONS [J].
VANDERHOUWEN, PJ ;
SOMMEIJER, BP .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (03) :595-617
12