Hewitt, L. L. and Hill, A. T., 2009. Algebraically stable general linear methods and the G-matrix. BIT Numerical Mathematics, 49 (1), pp. 93-111.
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The standard algebraic stability condition for general linear methods (GLMs) is considered in a modified form, and connected to a branch of Control Theory concerned with the discrete algebraic Riccati equation (DARE). The DARE theory shows that, for an algebraically stable method, there is a minimal G-matrix, G *, satisfying an equation, rather than an inequality. This result, and another alternative reformulation of algebraic stability, are applied to construct new GLMs with 2 steps and 2 stages, one of which has order p=4 and stage order q=3. The construction process is simplified by method-equivalence, and Butcher’s simplified order conditions for the case p≤q+1.
|Item Type ||Articles|
|Creators||Hewitt, L. L.and Hill, A. T.|
|Uncontrolled Keywords||discrete algebraic riccati equation,general linear methods,algebraic stability|
|Departments||Faculty of Science > Mathematical Sciences|
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