spectral.RK3#

class spectral.RK3[source]#

Bases: TimeIntegrator

3rd-order Strong Stability Preserving Runge-Kutta (SSP-RK3).

This explicit three-stage method preserves strong stability properties, making it particularly suitable for hyperbolic PDEs and problems requiring positivity preservation. The method is 3rd-order accurate in time.

Notes

The SSP property ensures that the numerical solution satisfies the same stability bounds as forward Euler under a modified time step restriction. This is particularly useful for problems with steep gradients or shocks.

References

Engsig-Karup, “Lecture 5: Initial Value Problems”, p. 63

Methods

`__init__`	Initialize time integrator.
`step`	Take one time step.

step(rhs: Callable, u: ndarray, t: float, dt: float) → ndarray[source]#

Take one time step.

Parameters:

rhsCallable: Right-hand side function f(u, t)
unp.ndarray: Current solution
tfloat: Current time
dtfloat: Time step

Returns:

np.ndarray: Solution at next time step