Study of spectral stability of generalized Runge-Kutta methods for the initial problem for transfer equation (Q2808423)

In this paper, the spectral stability of generalized Runge-Kutta methods of different accuracy orders is studied with regard to numerical integration of the initial problem for transfer equation. Approximate solutions obtained via different generalized Runge-Kutta methods are compared with the exact solution under complex-oscillating initial conditions with large modulo derivatives. It is shown that some classical finite-difference schemes of integration of the initial-boundary value problem for transfer equation result from a consecutive application of generalized and ordinary Runge-Kutta methods with respect to all independent variables.