Multivalue collocation methods free from order reduction

被引：16

作者：

D'Ambrosio, Raffaele ^{[1
]}

Paternoster, Beatrice ^{[2
]}

机构：

[1] Univ Aquila, Dept Engn & Comp Sci & Math, Laquila, Italy

[2] Univ Salerno, Dept Math, Fisciano, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 387卷 / 387期

关键词：

Stiff problems; Multivalue numerical methods; Collocation methods; Order reduction;

D O I：

10.1016/j.cam.2019.112515

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces multivalue collocation methods for the numerical solution of stiff problems. The presented approach does not exhibit the phenomenon of order reduction, typical of collocation based Runge-Kutta methods applied to stiff systems, since the introduced methods have uniform effective order of convergence on the overall integration interval. Examples of methods as well as numerical experiments on a selection of stiff problems are given. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：11

共 40 条

[1]

Burrage K., 1980, BIT (Nordisk Tidskrift for Informationsbehandling), V20, P185, DOI 10.1007/BF01933191

[2] Exponentially fitted IMEX methods for advection-diffusion problems [J].

Cardone, Angelamaria ;

D'Ambrosio, Raffaele ;

Paternoster, Beatrice .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 316 :100-108

[3] Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations [J].

Cash, JR .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2003, 459 (2032) :797-815

[4] Long-Term Stability of Multi-Value Methods for Ordinary Differential Equations [J].

D'Ambrosio, R. ;

Hairer, E. .

JOURNAL OF SCIENTIFIC COMPUTING, 2014, 60 (03) :627-640

[5] G-symplecticity implies conjugate-symplecticity of the underlying one-step method [J].

D'Ambrosio, R. ;

Hairer, E. ;

Zbinden, C. J. .

BIT NUMERICAL MATHEMATICS, 2013, 53 (04) :867-872

[6] General linear methods for y"=f(y(t)) [J].

D'Ambrosio, R. ;

Esposito, E. ;

Paternoster, B. .

NUMERICAL ALGORITHMS, 2012, 61 (02) :331-349

[7] Two-step almost collocation methods for ordinary differential equations [J].

D'Ambrosio, R. ;

Ferro, M. ;

Jackiewicz, Z. ;

Paternoster, B. .

NUMERICAL ALGORITHMS, 2010, 53 (2-3) :195-217

[8] Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems [J].

D'Ambrosio, Raffaele ;

Moccaldi, Martina ;

Paternoster, Beatrice .

COMPUTER PHYSICS COMMUNICATIONS, 2018, 226 :55-66

[9] Adapted numerical methods for advection-reaction-diffusion problems generating periodic wavefronts [J].

D'Ambrosio, Raffaele ;

Moccaldi, Martina ;

Paternoster, Beatrice .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (05) :1029-1042

[10] Numerical solution of reaction-diffusion systems of λ-ω type by trigonometrically fitted methods [J].

D'Ambrosio, Raffaele ;

Paternoster, Beatrice .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 294 :436-445

← 1 2 3 4 →