Stiff equation
![Explicit numerical methods exhibiting instability when integrating a stiff ordinary differential equation](/Images/godic/202502/13/StiffEquationNumericalSolvers.svg5118.png")
![The pink disk shows the stability region for the Euler method.](/Images/godic/202502/13/Stability_region_for_Euler_method.svg5118.png")
![The pink region is the stability region for the trapezoidal method.](/Images/godic/202502/13/Stability_region_for_trapezoidal_method.svg5118.png")
![The pink region is the stability region for the second-order Adams–Bashforth method.](/Images/godic/202502/13/Stability_region_for_AB2_method.svg5118.png")
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.