Solving Stiff Problems Using Generalized Picard Iterations

被引：0

作者：

Bobkov, V. V. ^{[1
]}

Faleichik, B. V. ^{[1
]}

Mandrik, P. A. ^{[1
]}

Repnikov, V. I. ^{[1
]}

机构：

[1] Belarusian State Univ, Minsk 220050, BELARUS

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2 | 2009年 / 1168卷

关键词：

Stiff differential equations; Picard iteration; principle of steadying; collocation methods; iterated Runge-Kutta methods;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main point of the talk is an alternative approach to the construction of numerical methods for stiff problems. It can be interpreted as a generalization of fixed-point iterations for implementation of implicit collocation methods. Proposed algorithms combine easy implementation and low cost of iterations with superior convergence properties on stiff problems, when compared to the conventional Picard iteration.

引用

页码：65 / 68

页数：4

共 11 条

[1] BAKHVALOV NS, 2004, NUMERICAL METHODS, P345
[2] BOBKOV VV, 2002, COMPUTATIONAL METHOD, V2, P354
[3] BOBKOV VV, 2008, VESTN BELORUSS GOS 1, P63
[4] BOBKOV VV, 1993, DIFF URAVN, V29, P689
[5] BOBKOV VV, 1967, IZV AKAD NAUK BS FMN, P27
[6] BUTCHER J. C., 1987, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods
[7] Faleichik B. V., 2008, COMPUTATIONAL METHOD, V8, P116
[8] Stiff differential equations solved by Radau methods
Hairer, E
Wanner, G
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 111 (1-2) : 93 - 111
[9] HAIRER E, 1999, SOLVING ORDINARY DIF, V2
[10] HAIRER E, 1993, SOLVING ORDINARY DIF, V1, P259

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