Stability Properties for Transformed Explicit Runge-Kutta Methods

A dominant factor is extracted from the Jacobian matrix. The semilinear system is transformed by a linear function and split into the dominant part and the residual part by using the dominant factor. The dominant part is exactly computed by evaluating only scalar functions exp, sin, and cos, and the residual part is approximately computed by the explicit Runge-Kutta method.It is shown that such a process is conditionally A-stable and conditionally B-stable