Second order time derivative - The Wave Equations

[dynamic-queries]

@xtalax Could you help me , implement this feature ? Any pointers on how to get started would be helpful

[xtalax]

Thanks for your interest in these tools.

So, what is needed is to recognize an initial condition for du/dt for any given u, take a look here. This is where we recogize the initial condition for u for any given u. Things to note, we only need to recognize ICs when an undiscretized dimension (usually t) is defined, hence the check that t == nothing. We recognize the IC by comparing the equation that the user supplied in the vector of bcs (see docs), checking if its lhs matches with the symbol for u at the initial time, defined for all dependant variables in initmaps. What we need is a dtinitmaps, that will recognize when the lhs is a time derivative at the initial time - the rhs will then be discretized as in the linked line.

Take a look here for what form ODESystem needs the initial derivative in (the call is here).

Let me know if you get stuck or have any questions :)

[xtalax]

Finally, we need tests for this.

[xtalax]

@dynamic-queries Have you made any progress on this? I'm thinking of attempting this if you haven't started.

[dynamic-queries]

@xtalax I was on vacation for the past weeks. But I have started this now. :D

[xtalax]

Note to self: Notify "George Gkountouras" when this is merged

[xtalax]

@dynamic-queries Can you submit a PR with what you've got so far so I can track progress and assist?

[xtalax]

A note, you should create any changes in a branch of your fork of this package, else you won't be able to submit a PR

[xtalax]

@dynamic-queries I'm going to start work on this if you don't have anything to share yet, all good?