Embedded adaptive step-size exponential RK for semilinear ODEs

[jtravs]

What kind of problems is it mostly used for? Please describe.

The exponential RK methods (e.g. ETDRK4) are excellent for solving semilinear ODEs but do not have adaptive time-stepping. See also discussion at: #2501

Describe the algorithm you’d like

There has been recent research on embedded exponential RK methods that provide an error estimate suitable for adaptive time stepping. A recent summary and method is proposed in https://arxiv.org/abs/2303.12139

Other implementations to know about

https://github.com/dealias/triad/blob/master/Exponential.h

References

Best ref:

• https://arxiv.org/abs/2303.12139

Some further discussion in e.g.

• https://arxiv.org/abs/1703.09622
• https://www.sciencedirect.com/science/article/abs/pii/S0021999114006743