On the order conditions of Runge-Kutta methods with higher derivatives

DOI10.1007/BF01390429zbMath0589.65057MaRDI QIDQ1074314

B. George

Publication date: 1986

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133147

zbMATH Keywords

Runge-Kutta methodsorder conditionselementary differentialsGaussButcherCrouzeixLobattoRadauTuran

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)

Related Items (10)

Explicit strong stability preserving multistage two-derivative time-stepping schemes ⋮ On implicit Runge-Kutta methods with higher derivatives ⋮ Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations ⋮ A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods ⋮ On explicit two-derivative two-step Runge-Kutta methods ⋮ High-order multiderivative time integrators for hyperbolic conservation laws ⋮ Derivation of three-derivative Runge-Kutta methods ⋮ Optimized low-dispersion and low-dissipation two-derivative Runge-Kutta method for wave equations ⋮ Trigonometrically fitted three-derivative Runge-Kutta methods for solving oscillatory initial value problems ⋮ New two-derivative implicit-explicit Runge-Kutta methods for stiff reaction-diffusion systems

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