Abstract
In this paper, we find some relationships among the coefficients matrices of second derivative general linear methods (SGLMs) which are sufficient conditions, but not necessary, to ensure the methods have Runge---Kutta stability (RKS) property. Considering these conditions, we construct some A--- and L---stable SGLMs with inherent RKS of orders up to five. Also, some numerical experiments for the constructed methods in variable stepsize environment are given.
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