Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:286

Article

Zhang, Hong¹  Sandu, Adrian¹  Tranquilli, Paul¹ 

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

关键词: Approximate matrix factorization;    Linearly implicit Runge-Kutta methods;    High order;    Reaction-diffusion equations;   

DOI  :  10.1016/j.cam.2015.03.005

来源: Elsevier

【 摘 要 】

Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate factorization usually leads to loss of accuracy, which makes it attractive only for low order time integration schemes. This paper discusses the application of approximate matrix factorization with high order methods; an inexpensive correction procedure applied to each stage allows to retain the high order of the underlying linearly implicit Runge-Kutta scheme. The accuracy and stability of the method's are studied. Numerical experiments on reaction-diffusion type problems of different sizes and with different degrees of stiffness illustrate the efficiency of the proposed approach. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free