منابع مشابه
Sequential second derivative general linear methods for stiff systems
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this p...
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General linear (GL) methods are numerical algorithms used to solve ODEs. The standard order conditions analysis involves the GL matrix itself and a starting procedure; however, a finishing method (F) is required to extract the actual ODE solution. The standard order analysis and stability are sufficient for the convergence of any GL method. Nonetheless, using a simple GL scheme, we show that th...
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We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to two-step Runge-Kutta methods, by Jackiewicz a...
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s of IWANASP, September 10 – 12, 2008, Ericeira, Portugal GENERAL LINEAR METHODS FOR VOLTERRA INTEGRAL EQUATIONS ZDZISÃlAW JACKIEWICZ Departament of Mathematics, Arizona State University Tempe, Arizona 85287, USA E-mail: [email protected] We investigate the class of general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations of the se...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.2852