SDIRK methods for stiff ODEs with oscillating solutions

DOI10.1016/S0377-0427(97)00056-3zbMath0887.65078WikidataQ127097603 ScholiaQ127097603MaRDI QIDQ1362410

O. Diekmann

Publication date: 25 May 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesdissipationdispersionRunge-Kutta methods\(A\)-stabilityoscillatory stiff problemsSDIRK methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

Efficient iterations for Gauss methods on second-order problems ⋮ GIP integrators for matrix Riccati differential equations ⋮ New optimized implicit-explicit Runge-Kutta methods with applications to the hyperbolic conservation laws ⋮ Exponentially fitted symmetric and symplectic DIRK methods for oscillatory Hamiltonian systems ⋮ Optimal high-order diagonally-implicit Runge-Kutta schemes for nonlinear diffusive systems on atmospheric boundary layer ⋮ Hybrid Runge-Kutta methods for ordinary differential equations ⋮ Optimization of high-order diagonally-implicit Runge-Kutta methods ⋮ Phase error analysis of implicit Runge-Kutta methods: new classes of minimal dissipation low dispersion high order schemes ⋮ Construction of SDIRK methods with dispersive stability functions ⋮ A new class of diagonally implicit Runge-Kutta methods with zero dissipation and minimized dispersion error ⋮ Study on banded implicit Runge-Kutta methods for solving stiff differential equations ⋮ Accuracy and linear stability of RKN methods for solving second-order stiff problems ⋮ An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies

Cites Work

• Phase properties of high order, almost P-stable formulae
• Chawla-Numerov method revisited
• Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional Schrödinger equation
• A low-order embedded Runge-Kutta method for periodic initial-value problems
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• An explicit hybrid method of Numerov type for second-order periodic initial-value problems
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Damping and phase analysis for some methods for solving second-order ordinary differential equations
• Phase-Lag Analysis of Implicit Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• A one-step method for direct integration of structural dynamic equations
• Explicit Runge-Kutta methods for initial value problems with oscillating solutions

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