Methods for special problems
Numerical integration of stiff differential equations
Article REF: AF653 V1
Methods for special problems
Numerical integration of stiff differential equations

Authors : Ernst HAIRER, Gerhard WANNER

Publication date: October 10, 2007 | Lire en français

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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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