ON CONVERGENCE OF THE PROJECTIVE INTEGRATION METHOD FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS

被引：0

作者：

MacLean, John ^{[1
]}

Gottwald, Georg A. ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2014年 / 12卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

Multi-scale integrators; projective integration; heterogeneous multiscale methods;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to center manifold theory. The error is shown to contain contributions associated with the numerical accuracy of the microsolver, the numerical accuracy of the macrosolver and the distance from the center manifold caused by the combined effect of micro-and macrosolvers, respectively. We corroborate our results by numerical simulations.

引用

页码：235 / 255

页数：21

共 50 条

[41] An adaptive discontinuous Galerkin method for very stiff systems of ordinary differential equations
Fortin, A.
Yakoubi, D.
APPLIED MATHEMATICS AND COMPUTATION, 2019, 358 : 330 - 347
[42] A NUMERICAL METHOD FOR SOLVING THE INITIAL VALUE PROBLEMS OF STIFF ORDINARY DIFFERENTIAL EQUATIONS
韩天敏
ScienceinChina,SerA., 1976, Ser.A.1976 (02) : 180 - 198
[43] Rational Homotopy Perturbation Method for solving stiff systems of ordinary differential equations
Biazar, Jafar
Asadi, Mohammad Ali
Salehi, Farideh
APPLIED MATHEMATICAL MODELLING, 2015, 39 (3-4) : 1291 - 1299
[44] On the convergence of sequences of ordinary differential equations
Vladimirov, AA
MATHEMATICAL NOTES, 2004, 75 (5-6) : 877 - 880
[45] On the Convergence of Sequences of Ordinary Differential Equations
A. A. Vladimirov
Mathematical Notes, 2004, 75 : 877 - 880
[46] The numerical simulation for stiff systems of ordinary differential equations
Darvishi, M. T.
Khani, F.
Soliman, A. A.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (7-8) : 1055 - 1063
[47] Predicting stiff ordinary differential equations with stiffness coefficient
Aliyu, B. K.
Nwojiji, C. U.
Kwentoh, A. O.
AUSTRALIAN JOURNAL OF MECHANICAL ENGINEERING, 2014, 12 (03) : 271 - 281
[48] Explicit methods in solving stiff ordinary differential equations
Ahmad, RR
Yaacob, N
Murid, AHM
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2004, 81 (11) : 1407 - 1415
[49] THE REGULAR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL-EQUATIONS
FEDORENKO, RP
DOKLADY AKADEMII NAUK SSSR, 1983, 273 (06): : 1318 - 1322
[50] A Numerical Algorithm for Solving Stiff Ordinary Differential Equations
Yatim, S. A. M.
Ibrahim, Z. B.
Othman, K. I.
Suleiman, M. B.
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013

← 1 2 3 4 5 →