A Quasi-Linear Implementation of High-Resolution Time Integration for the P_n Equations

We present an extension of our quasi-linear numerical method for the time-dependent spherical harmonics (P_n) equations. The extension involves adding time integration that is higher order than backward Euler, yet avoids artificial oscillations in the solution. This new approach mimics that of our previously presented quasi-linear spatial scheme in that we use a first-order step to determine in which parts of the problem we can use a high-order method. The first-order scheme we use for time integration is backward Euler, and the high-order method we implement is Crank-Nicolson. Results are presented that demonstrate the effectiveness and necessity of this approach.