TOWARDS EFFICIENT RUNGE-KUTTA METHODS FOR STIFF SYSTEMS

被引：28

作者：

BUTCHER, JC ^{[1
]}

CASH, JR ^{[1
]}

机构：

[1] UNIV LONDON IMPERIAL COLL SCI & TECHNOL,DEPT MATH,LONDON SW7 2AZ,ENGLAND

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1990年 / 27卷 / 03期

关键词：

D O I：

10.1137/0727044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A special class of implicit Runge-Kutta methods is developed for the numerical solution of stiff initial value problems. These formulae are derived from known singly implicit methods by adding one or more extra diagonally implicit stages. It is hoped that this modification of the original method will lead to an overall gain in efficiency, and an analysis of the advantages of making this enhancement is presented.

引用

页码：753 / 761

页数：9

共 50 条

[21] Numerical Approximation of Stiff Problems Using Efficient Nested Implicit Runge-Kutta Methods
Ur-Rehman, Attique
Rehman, Shafiq Ur
Ahmad, Junaid
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2019, 51 (02): : 1 - 19
[22] Explicit adaptive Runge-Kutta methods for stiff and oscillation problems
Skvortsov, L. M.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (08) : 1339 - 1352
[23] Stability of runge-kutta methods for stiff ordinary differential equations
Alexander, Roger K.
SIAM Journal on Numerical Analysis, 1994, 31 (04): : 1147 - 1168
[24] EFFICIENT IMPLEMENTATION OF IMPLICIT RUNGE-KUTTA METHODS
VARAH, JM
MATHEMATICS OF COMPUTATION, 1979, 33 (146) : 557 - 561
[25] Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Horvath, Z
APPLIED NUMERICAL MATHEMATICS, 1998, 28 (2-4) : 309 - 326
[26] THE RUNGE-KUTTA METHODS
THOMAS, B
BYTE, 1986, 11 (04): : 191 - &
[27] ON ORDER REDUCTION FOR RUNGE-KUTTA METHODS APPLIED TO DIFFERENTIAL ALGEBRAIC SYSTEMS AND TO STIFF SYSTEMS OF ODES
BURRAGE, K
PETZOLD, L
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (02) : 447 - 456
[28] Paired explicit Runge-Kutta schemes for stiff systems of equations
Vermeire, Brian C.
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 393 : 465 - 483
[29] CRITICAL-EVALUATION OF THE SEMI-IMPLICIT RUNGE-KUTTA METHODS FOR STIFF SYSTEMS
WEIMER, AW
CLOUGH, DE
AICHE JOURNAL, 1979, 25 (04) : 730 - 732
[30] Explicit Runge-Kutta Methods for Stiff Problems with a Gap in Their Eigenvalue Spectrum
Bocher, Philippe
Montijano, Juan, I
Randez, Luis
Van Daele, Marnix
JOURNAL OF SCIENTIFIC COMPUTING, 2018, 77 (02) : 1055 - 1083

← 1 2 3 4 5 →