Properties of four numerical schemes applied to a scalar nonlinear scalar wave equation with a GR-type nonlinearity
arXiv:gr-qc/0402085 · doi:10.1142/S021827180400502X
Abstract
We study stability, dispersion and dissipation properties of four numerical schemes (Iterative Crank-Nicolson, 3'rd and 4'th order Runge-Kutta and Courant-Fredrichs-Levy Non-linear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar non-linear wave equation with a type of non-linearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant-Fredrichs-Levy Non-linear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4'th order Runge-Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.
arXiv comment9 pages, 8 Postscript figures
References in corpus (4)
- Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
- On the Stability of the Iterated Crank-Nicholson Method in Numerical Relativity
- On the Numerical Stability of the Einstein Equations
- A scalar hyperbolic equation with GR-type non-linearity