Performance Improvements for Nuclear Reaction Network Integration

Aims: The aim of this work is to compare the performance of three reaction network integration methods used in stellar nucleosynthesis calculations. These are the Gear's backward differentiation method, Wagoner's method (a 2nd-order Runge-Kutta method), and the Bader-Deuflehard semi-implicit multi-step method. Methods: To investigate the efficiency of each of the integration methods considered here, a test suite of temperature and density versus time profiles is used. This suite provides a range of situations ranging from constant temperature and density to the dramatically varying conditions present in white dwarf mergers, novae, and x-ray bursts. Some of these profiles are obtained separately from full hydrodynamic calculations. The integration efficiencies are investigated with respect to input parameters that constrain the desired accuracy and precision. Results: Gear's backward differentiation method is found to improve accuracy, performance, and stability in integrating nuclear reaction networks. For temperature-density profiles that vary strongly with time, it is found to outperform the Bader-Deuflehard method (although that method is very powerful for more smoothly varying profiles). Wagoner's method, while relatively fast for many scenarios, exhibits hard-to-predict inaccuracies for some choices of integration parameters owing to its lack of error estimations.