Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the numerical time integration of a class of viscous wave equations by means of Runge–Kutta methods. The viscous wave equation is an extension of the standard second-order wave equation including advection–diffusion terms differentiated in time. The viscous wave equation can be very stiff so that for time integration traditional explicit methods are no longer efficient. A-Stable Runge–Kutta methods are then very good candidates for time integration, in particular diagonally implicit ones. Special attention is paid to the question how the A-Stability property can be translated to this non-standard class of viscous wave equations.
['Jan Verwer']
I am writing a research paper on a idea Runge–Kutta methods and viscous wave equations
[{"from": "human", "value": "I am writing a research paper on a idea Runge\u2013Kutta methods and viscous wave equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the numerical time integration of a class of viscous wave equations by means of Runge\u2013Kutta methods. The viscous wave equation is an extension of the standard second-order wave equation including advection\u2013diffusion terms differentiated in time. The viscous wave equation can be very stiff so that for time integration traditional explicit methods are no longer efficient. A-Stable Runge\u2013Kutta methods are then very good candidates for time integration, in particular diagonally implicit ones. Special attention is paid to the question how the A-Stability property can be translated to this non-standard class of viscous wave equations."}]