Singly diagonally implicit Runge-Kutta methods with an explicit first stage

DOI10.1023/B:BITN.0000046811.70614.38zbMath1066.65077OpenAlexW2079038427MaRDI QIDQ1770922

Anne Kværnø

Publication date: 7 April 2005

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:bitn.0000046811.70614.38

zbMATH Keywords

singular perturbationnumerical examplesstiff systemssingly diagonally implicit Runge-Kutta methodsexplicit first stage

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (32)

GIP integrators for matrix Riccati differential equations ⋮ Hybrid FEM-NN models: combining artificial neural networks with the finite element method ⋮ A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows ⋮ Computing the solutions of the van der Pol equation to arbitrary precision ⋮ Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver ⋮ 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 ⋮ Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations ⋮ Fourth-order Runge-Kutta schemes for fluid mechanics applications ⋮ Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method ⋮ Optimization of high-order diagonally-implicit Runge-Kutta methods ⋮ Automated translation and accelerated solving of differential equations on multiple GPU platforms ⋮ An efficient scheme for the implementation of implicit Runge-Kutta methods ⋮ Diagonally implicit Runge-Kutta methods for stiff problems ⋮ Variable step-size fractional step Runge-Kutta methods for time-dependent partial differential equations ⋮ A fourth-order approximate projection method for the incompressible Navier-Stokes equations on locally-refined periodic domains ⋮ On the effect of temporal error in high-order simulations of unsteady flows ⋮ Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems ⋮ An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods ⋮ Rosenbrock methods with an explicit first stage ⋮ Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems ⋮ Applications of doubly companion matrices ⋮ Low-Storage Integral Deferred Correction Methods for Scientific Computing ⋮ Implicit Runge-Kutta methods with explicit internal stages ⋮ Runge-Kutta research in Trondheim ⋮ Nonlinear higher-order transient solver for magnetic fluid hyperthermia ⋮ Adaptive nested implicit Runge-Kutta formulas of Gauss type ⋮ Automated Adjoints of Coupled PDE-ODE Systems ⋮ Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3 ⋮ An analysis of the Prothero-Robinson example for constructing new adaptive ESDIRK methods of order 3 and 4 ⋮ Transient thermal response with nonlocal radiation of a blast furnace main trough

This page was built for publication: Singly diagonally implicit Runge-Kutta methods with an explicit first stage