A low-dispersion and low-dissipation implicit Runge–Kutta scheme

A fourth-order, implicit, low-dispersion, and low-dissipation Runge–Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge–Kutta schemes. The scheme is designed to be A-stable for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries in the computational domain, and sound generation by reacting flows.