Comparison of numerical methods for the integration of the black hole geodesic equations

Details Comparison of numerical methods for the integration of the black hole geodesic equations Comparison of numerical methods for the integration of the black hole geodesic equations

Jun 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981jcoph..41..295s&link_type=abstract

Journal of Computational Physics, vol. 41, June 1981, p. 295-308.

Astronomy and Astrophysics

Astronomy

7

Black Holes (Astronomy), Boundary Value Problems, Gravitation Theory, Numerical Integration, Space-Time Functions, Stellar Rotation, Differential Equations, Electric Fields, Extrapolation, Geodesy, Gravitational Fields, Metric Space, Relativity, Runge-Kutta Method, Stellar Magnetic Fields

Scientific paper

Because of the complexity of the differential equations governing the geodesic paths, most analysis has concentrated on various specializations or particular symmetries, and the calculation of a general trajectory requires numerical integration. The reported study is concerned with an optimization of the calculational form of the equations. Possible numerical methods are discussed, and then compared by using two representative timelike tracks. The Runge-Kutta technique is not sufficiently reliable for all sets of initial conditions, nor is it sufficiently fast at high accuracies. The first difficulty, though not the second, would probably be cured by a more sophisticated approach. The Taylor series routine is distinctly slower than the Adams-Bashforth-Moulton (A) routine for only slightly better accuracy. The Gragg-Bulirsch-Stoer method cannot cope with the slight stiffness which can arise. The A routine emerges, therefore, as the favorite.

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