- Symmetric multistep methods over long times
2004/06/01 by Ernst Hairer, Christian Lubich · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Angular momentum #Applied mathematics #Classical mechanics #Computation #Differential equation #Error analysis #Linear multistep method #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Numerical analysis #Numerical methods for differential equations #Ordinary differential equation #Physics
- Strong Stability-Preserving High-Order Time Discretization Methods
2001/01/01 by Sigal Gottlieb, Chi-Wang Shu, Chi‐Wang Shu +1 · 133 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Backward Euler method #Class (philosophy) #Computational Fluid Dynamics and Aerodynamics #Computer science #Differential algebraic equation #Differential equation #Discretization #Euler equations #Euler method #Euler's formula #Hyperbolic partial differential equation #Linear multistep method #Mathematical analysis #Mathematics #Nonlinear system #Numerical methods for differential equations #Ordinary differential equation #Partial differential equation #Physics #Runge–Kutta methods #Stability (learning theory) #Total variation diminishing
- Numerical methods for ordinary differential equations in the 20th century
2000/12/01 by J. C. Butcher, J.C. Butcher · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Backward differentiation formula #Calculus (dental) #Collocation method #Computer science #Differential algebraic equation #Differential equation #Electromagnetic Simulation and Numerical Methods #Exact differential equation #Explicit and implicit methods #Exponential integrator #Initial value problem #Linear multistep method #Mathematical analysis #Mathematics #Numerical analysis #Numerical methods for differential equations #Numerical methods for ordinary differential equations #Ordinary differential equation #Runge–Kutta methods #Subject (documents)
- Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
1995/06/01 by Uri M. Ascher, Steven J. Ruuth, Brian Wetton +1 · 66 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Aliasing #Applied mathematics #Backward differentiation formula #Collocation (remote sensing) #Collocation method #Computational Fluid Dynamics and Aerodynamics #Computer science #Context (archaeology) #Convection–diffusion equation #Differential algebraic equation #Differential equation #Discretization #Explicit and implicit methods #Filter (signal processing) #Geometry #Grid #Linear multistep method #Mathematical analysis #Mathematics #Multigrid method #Numerical methods for differential equations #Ordinary differential equation #Partial differential equation #Spectral method
- Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
1979/03/01 by Peter Kaps, Peter Rentrop, P. Rentrop · 11 citations
Engineering · Mathematics · #Adaptive stepsize #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Backward differentiation formula #Computational Fluid Dynamics and Aerodynamics #Differential algebraic equation #Differential equation #Error analysis #Initial value problem #L-stability #Linear multistep method #Mathematical analysis #Mathematics #Numerical analysis #Numerical methods for differential equations #Numerical methods for ordinary differential equations #Ordinary differential equation #Runge–Kutta methods #Stiff equation #Truncation (statistics) #Truncation error
- A stability property of implicit Runge-Kutta methods
1975/12/01 by J. C. Butcher · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Artificial intelligence #Class (philosophy) #Computer science #Differential equation #Extension (predicate logic) #Linear multistep method #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Ordinary differential equation #Property (philosophy) #Runge–Kutta methods #Stability (learning theory)
- A special stability problem for linear multistep methods
1963/03/01 by Germund Dahlquist, Germund G. Dahlquist · 6 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Bounded function #Computer science #Constant (computer programming) #Differential equation #Geometry #Linear multistep method #Lipschitz continuity #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Product (mathematics) #Property (philosophy) #Stability (learning theory) #Statistics #Truncation (statistics) #Truncation error