Modern problems in astrophysics tend to require large, complex computational frameworks to solve many aspects of the system simultaneusly. Calculation of the energy production through nuclear reactions is typically one of those aspects. The use of standard nuclear burning algorithms will take up the majority of the computational time with all but the smallest of networks. The explicit asymptotic method has shown promise in computing large networks faster than existing methods in various environments while retaining accuracy. The purpose of this thesis is to show that this method can be successfully used to solve complex systems using a network of realistic size in a reasonable amount of time, and to investigate some problems in the flame propagation for a Type Ia, which have never been investigated with a realistic network.

Modern problems in astrophysics tend to require large, complex computational frameworks to solve many aspects of the system simultaneusly. Calculation of the energy production through nuclear reactions is typically one of those aspects. The use of standard nuclear burning algorithms will take up the majority of the computational time with all but the smallest of networks. The explicit asymptotic method has shown promise in computing large networks faster than existing methods in various environments while retaining accuracy. The purpose of this thesis is to show that this method can be successfully used to solve complex systems using a network of realistic size in a reasonable amount of time, and to investigate some problems in the flame propagation for a Type Ia, which have never been investigated with a realistic network.