A Dissipative Algorithm for Wave-like Equations in the Characteristic Formulation

1998/11/30 by Luis Lehner · 4 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Model Reduction and Neural Networks #Numerical methods for differential equations #gr-qc

paper · pdf · doi:10.1006/jcph.1998.6137

23 pages, 7 figures

arxiv created 1998/11/30 · openalex publication_date 1999/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the highly nonlinear regime where previous methods have failed to give a stable evolution in three dimensions. The algorithm presented in this work is directly applicable to hyperbolic systems proper of electromagnetism, Yang–Mills, and general relativity theories. We carry out an analysis of the stability of the algorithm and test its properties with linear waves propagating on a Minkowski background and the scattering off a Scwharszchild black hole in general relativity.

Citations

• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time

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