Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Storage Reduction for Runge-Kutta Codes
ACM Transactions on Mathematical Software (TOMS)
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations
SIAM Journal on Scientific Computing
On some new low storage implementations of time advancing Runge-Kutta methods
Journal of Computational and Applied Mathematics
Strong Stability Preserving Two-step Runge-Kutta Methods
SIAM Journal on Numerical Analysis
| Hi-index | 31.45 |
Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties.