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Více informací o knize analysis of the TR-BDF2 integration scheme

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• Anotace
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Anotace knihy

We intend to try to better our understanding of how the combined L-stable Trapezoidal Rule with the second order Backward Di erence Formula (TR-BDF2) integrator and the standard A-stable Trapezoidal integrator perform on systems of coupled non-linear partial differential equations (PDEs). It was originally Professor Klaus-Jurgen Bathe who suggested that further analysis was needed in this area. We draw attention to numerical instabilities that arise due to insufficient numerical damping from the Crank-Nicolson method (which is based on the Trapezoidal rule) and demonstrate how these problems can be rectified with the TR-BDF2 scheme. Several examples are presented, including an advection-diffusion-reaction (ADR) problem and the (chaotic) damped driven pendulum. We also brie y introduce how the ideas of splitting methods can be coupled with the TR-BDF2 scheme and applied to the ADR equation to take advantage of the excellent modern day explicit techniques to solve hyperbolic equations.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics

• Plný název: analysis of the TR-BDF2 integration scheme
• Autor: Sohan Dharmarajah
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 84
• EAN: 9783639223453
• ISBN: 3639223454
• ID: 06830152
• Nakladatelství: VDM Verlag
• Hmotnost: 136 g
• Rozměry: 229 × 152 × 5 mm
• Datum vydání: 23. December 2009

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