Stiff equation

Explicit numerical methods exhibiting instability when integrating a stiff ordinary differential equation

The pink disk shows the stability region for the Euler method.

The pink region is the stability region for the trapezoidal method.

The pink region is the stability region for the second-order Adams–Bashforth method.

In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution.

单词	Stiffness ratio
释义	Stiffness ratio 英语百科 Stiff equation In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution.
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Stiffness ratio

Stiff equation