Solving first order PDE in maxima

Question

I have recently started working on maxima.

Can somebody tell me whether we can solve Cauchy problem for first order PDE in maxima or not?

Also, please advice some good books for learning maxima, especially for PDE problems like heat equation, wave equation.

Thanks

Answer 1

Unfortunately there are no built-in functions like Mathematica NDSolve, in Maxima at this moment and you have to code it up yourself. There are like a zillion different numerical methods out there for solving PDEs, and it all boils down to your equations and boundary/initial conditions. finite difference, finite element, finite volume, expansion series ... It is pointless to argue which one is better than the other, unless you specify your problem.

I wouldn't recommend Maxima for intensive numerical calculations though. Maxima is a great tool for symbolic calculation but IMHO not great at numerical performance.

There is a very nice book recommended at Maxima documentations:

Kai Velten: Mathematical Modeling and Simulation, Wiley-VCH, 2009.

There you can find examples of PDE numerical solution as well as Maxima examples.