What is best ODE solver for stiff problem?

#1

Dear all,

I know @ivanpribec has a stiff3 ODE solver for stiff problem,

Is there some other stiff ODE solver too?

@prince_mahajan point to Hairer solver too,

http://www.unige.ch/~hairer/software.html

How is stiff3 algorithm compare with Hairer method? In terms of accuracy and speed?

Thank you very much in advance!

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#2

DIRK solvers are rather thoroughly investigated in the recent paper

Without any special needs, I found the suggested default solver “ESDIRK4(3)6L[2]SA” pretty good.
Speed greatly depends on how fast the underlying implicit equation can be solved (by Newton?) and how good the adaptive time step control can be tuned.

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#3

Thank you @martin !
Welcome to the community!

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#4

What is best ODE solver for stiff problem?

It depends on the problem. DifferentialEquations.jl has a great summary of recommended methods ODE Solvers · DifferentialEquations.jl

I do atmospheric chemical kinetics involving 10,000s ODEs, which are very stiff. For this problem, one of the best methods is CVODE BDF with the banded matrix solver. CVODE is written in C but has an excellent Fortran interface.

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