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3. Methods for special problems
In practice, we often come across very large stiff differential equations for which numerical solution of the nonlinear system using the implicit method is very costly or even impossible. It also happens that the stiffness of the differential equation is present only in a small part of the equation, so we'd like to take advantage of this situation. This section presents some interesting approaches to these particular problems.
3.1 Explicit methods with long stability regions
According to the Jeltsch-Nevanlinna theorem mentioned in paragraph , there is no explicit method that is superior, from the point of view of stability, to any other explicit method for all problems. However, in the presence of information on the location of the eigenvalues,...
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Methods for special problems
References
General works
Computer programs
For solving stiff differential equations, there are some excellent public domain programs available for download from the Internet.
n http://www.unige.ch/~hairer/software.html
RADAU5 is based on an implicit Runge-Kutta method (Radau IIA, § 2.1.1) of order 5.
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Authors' Internet addresses
Ernst HAIRER
e-mail : [email protected]
Gerhard WANNER
email : [email protected]
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