Help me outperform Matlab in numerical solution of semidiscretized PDE system as much as possible

[ChrisRackauckas]

@RobertS

In the equation for r_R rRr_R , you see that I added a smooth multiplicative term making sure that the reaction rate approaches zero when the reactant concentration reaches zero. This is my standard approach, which usually works in my Matlab implementations. In the vicinity of zero concentration, when the smooth multiplicator becomes active, the solvers are forced to take small steps, leading to reduced performance. I am very open to criticism here and would love to hear better approaches (callbacks?) that work well in Julia in such situations.

Handling Instability When Solving ODE Problems

Thanks for the example. I will share as little as possible but just a snippet in order to explain what’s going on to others. This is a good teaching opportunity. I was able to find out that the problem is that, in the statement k9*X3/(k10*k11/(k12*(1.-min(1.,k13+k14*X5))) + X3) when X3 and X5 are dual numbers, the value of k11/(k12*(1.-min(1.,k13+k14*X5))) is NaN for the derivative components when the condition makes it the constant 1.0 (since the derivative of the minimum of in the denominat…

In general, the FAQ and PSA are helpful.

https://diffeq.sciml.ai/stable/basics/faq/

PSA: How to help yourself debug differential equation solving issues

Debugging differential equation solver issues almost always boils down to doing the same thing, so this is a summary to help you out. For more information on specific issues, check out the FAQ section of the DifferentialEquations.jl documentation which highlights common issues and questions: https://diffeq.sciml.ai/dev/basics/faq/ How do I debug why the differential equation solver is diverging? dt <= dtmin. Aborting. There is either an error in your model specification or the true solution i…