Extrapolated Implicit-Explicit Runge-Kutta Methods

被引：29

作者：

Cardone, Angelamaria ^{[1
]}

Jackiewicz, Zdzislaw ^{[2
,3
]}

Sandu, Adrian ^{[4
]}

Zhang, Hong ^{[4
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, I-84084 Fisciano, SA, Italy

[2] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA

[3] AGH Univ Sci & Technol, Krakow, Poland

[4] Virginia Polytech Inst & State Univ, Dept Comp Sci, Blacksburg, VA 24061 USA

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2014年 / 19卷 / 01期

基金：

美国国家科学基金会;

关键词：

non-stiff and stiff processes; extrapolated IMEX methods; Runge-Kutta methods; error and stability analysis; construction of highly stable methods; INTEGRAL-EQUATIONS; NORDSIECK METHODS; HIGH-ORDER; IMPLEMENTATION; CONSTRUCTION;

D O I：

10.3846/13926292.2014.892903

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a new class of implicit-explicit singly diagonally implicit Runge-Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was first proposed by the authors in context of implicit-explicit general linear methods.

引用

页码：18 / 43

页数：26

共 28 条

[1] [Anonymous], 2002, THESIS U AUCKLAND NZ
[2] [Anonymous], THESIS ARIZONA STATE
[3] Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Ascher, UM
Ruuth, SJ
Spiteri, RJ
[J]. APPLIED NUMERICAL MATHEMATICS, 1997, 25 (2-3) : 151 - 167
[4] Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
Bartoszewski, Z
Jackiewicz, Z
[J]. APPLIED NUMERICAL MATHEMATICS, 2005, 53 (2-4) : 149 - 163
[5] Construction of two-step Runge-Kutta methods of high order for ordinary differential equations
Bartoszewski, Z
Jackiewicz, Z
[J]. NUMERICAL ALGORITHMS, 1998, 18 (01) : 51 - 70
[6] Implementation of explicit Nordsieck methods with inherent quadratic stability
Bras, Michal
Cardone, Angelamaria
D'Ambrosio, Raffaele
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2013, 18 (02) : 289 - 307
[7] Construction of Efficient General Linear Methods for Non-Stiff Differential Systems
Bras, Michal
Cardone, Angelamaria
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2012, 17 (02) : 171 - 189
[8] Butcher J. C., 2003, Numerical Methods for Ordinary Differential Equations, V2nd, DOI DOI 10.1002/9780470753767
[9] A parallel algorithm for large systems of Volterra integral equations of Abel type
Capobianco, G.
Cardone, A.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) : 749 - 758
[10] A fast iterative method for discretized Volterra-Fredholm integral equations
Cardone, A
Messina, E
Russo, E
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 189 (1-2) : 568 - 579

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