Abstract
Algebraic stability has been already studied for general linear methods (GLMs) to analyze the behavior of the methods applying to the non-linear problems. We discuss this concept for the class of second derivative GLMs (SGLMs) and derive sufficient conditions on the coefficients of these methods guaranteeing the algebraic stability of the methods. Moreover, by defining irreducible SGLMs, we analyze algebraically stable SGLMs which are also irreducible. Then, we construct some examples of the methods up to order four.
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