Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a generalized solution of the Riemann problem for a general resonant nonlinear balance law, and  prove the convergence of the 2 x 2 Godunov numerical method based on these solutions. In particular,  obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the Riemann problem, and an interesting multiplicity of time-asymptotic wave patterns is observed and characterized.
['Eli L. Isaacson', 'Blake Temple']
I am writing a research paper on a idea Convergence of the 2×2 Godunov method for a general resonant nonlinear balance law
[{"from": "human", "value": "I am writing a research paper on a idea Convergence of the 2\u00d72 Godunov method for a general resonant nonlinear balance law"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a generalized solution of the Riemann problem for a general resonant nonlinear balance law, and  prove the convergence of the 2 x 2 Godunov numerical method based on these solutions. In particular,  obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the Riemann problem, and an interesting multiplicity of time-asymptotic wave patterns is observed and characterized."}]