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Solving stiff differential equations for simulation

✍ Scribed by T.D. Bui

Publisher: Elsevier Science
Year: 1981
Tongue: English
Weight: 540 KB
Volume: 23
Category: Article
ISSN: 0378-4754
DOI: 10.1016/0378-4754(81)90052-5

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✦ Synopsis

Computer simulation

of dynamic systems very often leads to the solution of a set of stiff ordinary differential equations.

The solution of this set of equations involves the eigenvalues of its Jacobian matrix.

The greater the spread in eigenvalues, the more time consuming the solutions become when existing numerical methods are employed.

Extremely stiff differential equations can become a very serious problem for some systems, rendering accurate numerical solutions completely uneconomic.

In this paper, we propose new techniques for solving extremely stiff systems of differential equations.

These algorithms are based on a class of implicit Runge-Kutta procedure with complete error estimate.

The new techniques are applied to solving mathematical models of the relaxation problem behind blast waves.

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