Solvers that are designed for stiff ODEs, known as stiff solvers, typically do more work per step. This is why ode45 is classified as a nonstiff solver along with ode23, ode78, ode89, and ode113. The problem that stiff ODEs pose is that explicit solvers (such as ode45) are untenably slow in achieving a solution. This can lead to the solver failing the integration, but even if it succeeds it will take a very long time to do so.Įquations that cause this behavior in ODE solvers are said to be stiff. These step sizes can be so small that traversing a short time interval might require millions of evaluations. For some ODE problems, the step size taken by the solver is forced down to an unreasonably small level in comparison to the interval of integration, even in a region where the solution curve is smooth.
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