A Note on Fourth-Order Time Stepping for Stiff PDE via ... - HIKARI Ltd
A Note on Fourth-Order Time Stepping for Stiff PDE via ... - HIKARI Ltd
A Note on Fourth-Order Time Stepping for Stiff PDE via ... - HIKARI Ltd
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<strong>Time</strong> stepping <strong>for</strong> stiff <strong>PDE</strong> <strong>via</strong> spectral method 1887<br />
Fig. 2. <strong>Time</strong> evoluti<strong>on</strong> <strong>for</strong> the viscous Burgers’ equati<strong>on</strong> ( 0), where the x axis<br />
runs from x = -3 to x = 3, and the t-axis runs from t = 0 to t = 150.<br />
4. C<strong>on</strong>clusi<strong>on</strong><br />
This note overcomes a stiff type problem <strong>via</strong> the exp<strong>on</strong>ential method. We<br />
have utilized effectively the exp<strong>on</strong>ential time differencing Runge-Kutta 4 method<br />
(ETDRK4) to solve the diag<strong>on</strong>al example of Burgers’ equati<strong>on</strong> (inviscid and<br />
viscous <strong>for</strong>ms) with Fourier's trans<strong>for</strong>mati<strong>on</strong>. By implementing the Matlab codes,<br />
we have successfully solved numerically the Burgers equati<strong>on</strong>. In future<br />
publicati<strong>on</strong>, we hope to employ these techniques to more complicated n<strong>on</strong>diag<strong>on</strong>al<br />
case, <strong>for</strong> example the Fisher equati<strong>on</strong>, which is a well known equati<strong>on</strong><br />
from the research areas in heat & mass transfer, populati<strong>on</strong> dynamics and ecology.<br />
Acknowledgement<br />
Reza is thankful to UTM <strong>for</strong> Internati<strong>on</strong>al Doctoral Fund (IDF). This research is<br />
partially funded by MOHE FRGS Vote no. 78675 and UTM RUG Vot. No.05J13.
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