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Introduction to 3+1 Numerical Relativity$
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Miguel Alcubierre

Print publication date: 2008

Print ISBN-13: 9780199205677

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199205677.001.0001

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NUMERICAL METHODS

NUMERICAL METHODS

Chapter:
(p.318) 9 NUMERICAL METHODS
Source:
Introduction to 3+1 Numerical Relativity
Author(s):

Miguel Alcubierre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199205677.003.0009

There are many ways to solve partial differential equations numerically. The most popular methods are: finite differencing, finite elements, and spectral methods. This chapter describes the main ideas behind finite differencing methods, since this is the most commonly used approach in numerical relativity. It focuses on methods for the numerical solution of systems of evolution equations of essentially ‘hyperbolic’ type, and does not deal with the solution of elliptic equations, such as those needed for obtaining initial data.

Keywords:   finite differencing, wave equation, finite difference approximation, implicit approximation, boundary conditions, dissipation, convergence testing

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