A six-field, nonlinear, reduced magnetohydrodynamics model containing the shear Alfv ́en wave and electron and ion heat conduction along magnetic fields is solved by using Jacobian-free Newton-Krylov (JFNK) methods and nonlinear GMRES (NGMRES). Physics-based preconditioning based on analytic Schur factorization of a simplified Jacobian is found to result in an order of magnitude reduction in runtime over unpreconditioned JFNK, and NGMRES is shown to significantly reduce runtime while requiring only the nonlinear function evaluation. This work is described in detail in our 2012 paper.