High accurate NRK and MWENO scheme for nonlinear degenerate parabolic PDEs

In this paper, we propose a stable high accurate hybrid scheme based on nonstandard Runge-Kutta (NRK) and modified weighted essentially non-oscillatory (MWENO) techniques for nonlinear degenerate parabolic partial differential equations. The necessary stability condition for the combination of a Runge-Kutta and MWENO scheme is given. The stability condition provides a renormalization function such that mixture of explicit NRK and MWENO scheme is unconditionally stable. Novel scheme recovers the sixth order convergent at points of inflection and prevents the appearance of spurious solutions close to discontinuities. The good performance of this scheme is illustrated through five examples. Numerical results are presented.