 |
Center for Nonlinear Studies |
Parabolic operators play an important role in simulating many physical systems, but they often represent a sub-dominant part of the physical system. Parabolic operators often require very short explicit time-steps to maintain stability, necessitating either taking many short time-steps, or solving the parabolic components using an implicit method, both of which are computationally costly. The Runge-Kutta-Legendra (RKL) method solves this problem by combining many Runge-Kutta like sub-steps to achieve extended stability in time. Specifically, RKL is capable of integrating to a time proportional to n^2 explicit time-steps when only n stages are used. RKL is accurate, stable and monotone for all sub-stages and for all times less than the stability limit, which make it useful for operators with spatially- and temporally-varying coefficients. These properties make RKL ideal for solving parabolic PDE systems and systems with mixed parabolic and hyperbolic operators.
Host: Misha Shashkov