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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
An analysis of the TR-BDF2 integration scheme

An analysis of the TR-BDF2 integration scheme

Dharmarajah, Sohan

Paperback

General Mathematics

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ISBN10: 3639223454
ISBN13: 9783639223453
Publisher: Blues Kids Of Amer
Published: Dec 23 2009
Pages: 84
Weight: 0.30
Height: 0.20 Width: 6.00 Depth: 9.00
Language: English
We intend to try to better our understanding of how the combined L-stable 'Trapezoidal Rule with the second order Backward Difference 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 briefly 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.

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