Diagonally implicit Runge-Kutta methods for stiff problems

DOI10.1134/s0965542506120098MaRDI QIDQ6200644

L. M. Skvortsov

Publication date: 1 March 2024

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

Full work available at URL: http://mathnet.ru/eng/zvmmf367

zbMATH Keywords

diagonally implicit Runge-Kutta methodsstiff problemsODEESDIRKSDIRK

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (10)

Stability analysis of a diagonally implicit scheme of block backward differentiation formula for stiff pharmacokinetics models ⋮ Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems ⋮ Singly implicit diagonally extended Runge-Kutta methods of fourth order ⋮ How to avoid accuracy and order reduction in Runge-Kutta methods as applied to stiff problems ⋮ Stability and error estimates of high order BDF-LDG discretizations for the Allen-Cahn equation ⋮ High-order locally a-stable implicit schemes for linear ODEs ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems ⋮ High-order accurate bicompact schemes for solving the multidimensional inhomogeneous transport equation and their efficient parallel implementation ⋮ Implicit Runge-Kutta methods with explicit internal stages ⋮ Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3

Cites Work

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• Quasi stage order conditions for SDIRK methods
• Singly diagonally implicit Runge-Kutta methods with an explicit first stage
• A class of low order DIRK methods for a class of DAEs
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Analysis and implementation of TR-BDF2
• \(L\)-decremented ROW method of third-order accuracy
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• A four-stage index 2 diagonally implicit Runge-Kutta method
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