Construction of general linear methods with Runge-Kutta stability properties

We describe the construction of explicit general linear methods of order p and stage order q = p with s = p + 1 stages which achieve good balance between accuracy and stability properties. The conditions are imposed on the coefficients of these methods which ensure that the resulting stability matrix has only one nonzero eigenvalue. This eigenvalue depends on one real parameter which is related to the error constant of the method. Examples of methods are derived which illustrate the application of the approach presented in this paper.