implement solveODE

[dvd101x]

Hi, this includes a function to do numeric integration of ordinary differential equations in a similar fashion to scipy.integrate.solve_ivp.

It includes Runge-Kutta methods with variable step size 'RK45' and 'RK23'.

Some ideas for the future are:

• Include an array like for tolerance for each element in the state (currently it calculates only with the maximum value of the error)
• Include tEval option so that it guaranties that every one of the times in that array are returned and no other one (internal steps might vary).
• args: include extra arguments to the function so if a function already exists of the form myF(t, y, a, b, c) we could include in options {args: [a, b, c]} instead of making a new function of the form f(t, y)
• Once there is a root finding algorithm in numeric, implement other methods like:
  • BDF
  • LSODA

[josdejong]

Thanks a lot David, this looks really neat. The code looks very clean and easy to follow. I made a couple of inline comments, can you have a look at those? (nothing big)

[josdejong]

O, and I see one of the CI tests fails because there are no embedded docs. Can you add a file solveODE.js there and list it in src/expression/embeddedDocs.js? Thanks!

[dvd101x]

Hi Jos, thank you for your through review.

Everything is very clear, I will work on that, I just included a few comments regarding error messages.

[dvd101x]

Thank you very much for the review. Here is an overview of the changes

• It has embedded docs
• Included the returned object in the jsdocs
• It works with matrices and returns matrices
• Throws some more specific errors regarding
  • max iter reached
  • tspan has no numeric or unit values
  • method name
• Simplifies most tests using functions previously implemented
• Included a more challenging function to test f(t, y) = y - t instead of f(t, y) = y

Here is the bad part:

• It doesn't work with big numbers yet

[dvd101x]

Now it works with big numbers

[dvd101x]

These are the recent changes:

• The logic was simplified a bit by forcing:
  • maxStep and firstStep to be positive
  • minStep to be positive or zero
• Included tests for time related variables like tspan[0], tspan[1], minStep, maxStep and firstStep
• I encountered an error where I thought isNumeric included only number and bigNumber. So I used something else
• Fixed a typo with deltaB

Some drawbacks is that now instead of just solving some cases it throws an error, bit it might be ok.

[josdejong]

Thanks for the updates David. All looks good to go 👌

[dvd101x]

That's great news! Thanks!

[josdejong]

Published now in v11.9.0.