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

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 ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff problems $K_{σ,τ}$ 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 $K_{σ,0}$ 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 and Yue and and 19819 and and Chao Yue and Aiguo and Xiao and and 19820 and and Aiguo Xiao and Hongliang and Liu and and 19821 and 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 ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff problems $K_{σ,τ}$ 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 $K_{σ,0}$ 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 - Yue , Chao AU - Xiao , Aiguo AU - Liu , Hongliang JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 472 EP - 495 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m230 UR - https://global-sci.org/intro/article_detail/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 ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff problems $K_{σ,τ}$ 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 $K_{σ,0}$ 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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