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Properties of four numerical schemes applied to a scalar nonlinear scalar wave equation with a GR-type nonlinearity | | Jakob Hansen
; Alexei Khokhlov
; Igor Novikov
; | | Date: |
19 Feb 2004 | | Journal: | Int.J.Mod.Phys. D13 (2004) 961 | | Subject: | gr-qc | | 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. | | Source: | arXiv, gr-qc/0402085 | | Services: | Forum | Review | PDF | Favorites | |
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