Abstract
Theory of general linear methods (GLMs) for the numerical solution of autonomous system of ordinary differential equations of the form y′=f(y) is extended to include the second derivative y″=g(y):=f′(y)f(y). This extension of GLMs is called second derivative general linear methods (SGLMs). In this paper we will construct two-stage A- and L-stable SGLMs of order p and stage order q=p up to six with low error constants. We will show the efficiency of the proposed methods by implementing on some well-known stiff problems.
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