Numerical SolveTensors?

[Jack Smithe]

Does anyone know if there is a numerical equivalent of the SolveTensors function in xAct?

I have a fairly complicated covariant field Lagrangian density, for which I used xAct to apply Euler-Lagrange to find the field equations in tensor form. The resulting (tensor-form) PDE field equations now have too many terms and summation indices for me to feasibly put into array form by hand to use DSolve.

I found SolveTensors, but it appears to be analytical. I doubt there are very many analytical solutions to these field equations, and mathematica seems to be stalling trying to solve it anyway. I'm wondering if there might be a numerical form of SolveTensors, whereby I might be able to input my PDE field equations in their tensor form and have it solve the PDEs numerically. Any help would be greatly appreciated! Thanks!

[Jose]

Hi,

No, there is no automatic support in xAct for solving PDEs numerically. The general case of this involves choices of coordinates, of numerical methods, of initial and boundary conditions, etc, so it can get very complicated. Have a look at the Einstein Toolkit ( https://einsteintoolkit.org/ ), for example, to see if you can solve your equations there.

Cheers,

Jose.