Adaptive step size control for ImplicitDiscreteProblem via Newton convergence estimate #2666

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termi-official opened this issue Apr 3, 2025 · 0 comments

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termi-official commented Apr 3, 2025

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

Parameter continuation and homotopy path problems in PDE-land.

Describe the algorithm you’d like

Use OrdinaryDiffEqNonlinearSolve in ImplicitDiscreteSolve to (PID) control the step length with the help of Newton convergence rate estimates as proposed by https://link.springer.com/chapter/10.1007/978-3-642-23899-4_5

Other implementations to know about

Thunderbolt.jl has a custom time integrator with a custom solver and custom controller which we can upstream into OrdinaryDiffEq step by step.

References

Deuflhard, Newton Methods for Nonlinear Problems

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