Singly implicit diagonally extended Runge-Kutta methods of fourth order

DOI10.1134/S0965542514050133zbMath1313.65186MaRDI QIDQ2940477

L. M. Skvortsov

Publication date: 26 January 2015

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

stiff problemsdifferential-algebraic problemsimplicit diagonally extended Runge-Kutta methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80) Numerical methods for stiff equations (65L04)

Related Items (4)

How to avoid accuracy and order reduction in Runge-Kutta methods as applied to stiff problems ⋮ An embedded formula of the Chebyshev collocation method for stiff problems ⋮ Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems

Uses Software

• TR-BDF2
• RODAS
• DESI

Cites Work

• A new type of singly-implicit Runge-Kutta method
• Singly diagonally implicit Runge-Kutta methods with an explicit first stage
• Convergence of Runge-Kutta methods for differential-algebraic systems of index 3
• Analysis and implementation of TR-BDF2
• Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2
• Diagonally implicit Runge—Kutta methods for differential algebraic equations of indices two and three
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• DESI methods for stiff initial-value problems
• An efficient scheme for the implementation of implicit Runge-Kutta methods
• Diagonally implicit Runge-Kutta methods for stiff problems
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