Volume 7, Issue 4
Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems

Chao Yue, Aiguo Xiao, & Hongliang Liu

Adv. Appl. Math. Mech., 7 (2015), pp. 472-495.

Published online: 2018-05

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  • Abstract

In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of (θ, p¯,q¯)-algebraic stability of ARK methods for a class of stiff problems Kσ,τ is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for Kσ,0 are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.

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@Article{AAMM-7-472, author = {Chao Yue, Aiguo Xiao, and Hongliang Liu}, title = {Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {4}, pages = {472--495}, abstract = {

In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of (θ, p¯,q¯)-algebraic stability of ARK methods for a class of stiff problems Kσ,τ is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for Kσ,0 are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m230}, url = {http://global-sci.org/intro/article_detail/aamm/12059.html} }
TY - JOUR T1 - Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems AU - Chao Yue, Aiguo Xiao, & Hongliang Liu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 472 EP - 495 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2013.m230 UR - https://global-sci.org/intro/aamm/12059.html KW - AB -

In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of (θ, p¯,q¯)-algebraic stability of ARK methods for a class of stiff problems Kσ,τ is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for Kσ,0 are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.

Chao Yue, Aiguo Xiao, & Hongliang Liu. (1970). Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems. Advances in Applied Mathematics and Mechanics. 7 (4). 472-495. doi:10.4208/aamm.2013.m230
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