Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection–reaction–diffusion systems.  provide a partial linearization under which a sufficient condition emerges that guarantees stability in this context. The stability behavior of these systems is then closely analyzed relative to Runge–Kutta Chebyshev (RKC) and strong stability preserving (RKSSP) temporal discretizations over a nonlinear system of reactive compressible gases arising in the study of atmospheric chemistry.
['Craig Michoski', 'Alen Alexanderian', 'Cristian Paillet', 'Ethan J. Kubatko', 'Clint Dawson']
I am writing a research paper on a idea Stability of Nonlinear Convection–Diffusion–Reaction Systems in Discontinuous Galerkin Methods
[{"from": "human", "value": "I am writing a research paper on a idea Stability of Nonlinear Convection\u2013Diffusion\u2013Reaction Systems in Discontinuous Galerkin Methods"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection\u2013reaction\u2013diffusion systems.  provide a partial linearization under which a sufficient condition emerges that guarantees stability in this context. The stability behavior of these systems is then closely analyzed relative to Runge\u2013Kutta Chebyshev (RKC) and strong stability preserving (RKSSP) temporal discretizations over a nonlinear system of reactive compressible gases arising in the study of atmospheric chemistry."}]