what PDE types can solvepde solve

What PDE types can solvepde solve?

Is solvepde just femlab in the past?

Answer 1

[KALYAN ACHARJYA]

The solvepde function in MATLAB is part of the Partial Differential Equation Toolbox, which is used to solve partial differential equations (PDEs) numerically using the finite element method (FEM).

Is solvepde Just Femlab from the Past?

No, solvepde is not FEMLAB

[feynman feynman]

What PDE types can solvepde solve?

[Torsten]

m * d^2u/dt^2 + d * du/dt - div(c*grad u) + a * u = f

[feynman feynman]

@Torsten thanks, so it's also accurate for hyperbolic ones?

[Torsten]

If your hyperbolic equation fits into the above scheme (e.g. the usual wave equation), it should work:

m = 1, d = 0, c = 1, a = 0, f = 0.

General hyperbolic equations of the form

du/dt + grad(f(u)) = s

can not be solved with the PDE Toolbox.

[feynman feynman]

thank you how about du/dt+du/dx=0?

[Torsten]

Can you find m, d, c, a and f such that

m * d^2u/dt^2 + d * du/dt - div(c*grad u) + a * u = f

becomes

du/dt + du/dx = du/dt + grad(u) = 0

?

Technically, you can set m = 0, d = 1, c = 0, a = 0 and f = -du/dx = -grad(u).

This seems to be possible: Stated from the documentation of the PDE Toolbox:

Coefficients

The coefficients m, d, c, a, and f can be functions of location (x, y, and, in 3-D, z), and, except for

eigenvalue problems, they also can be functions of the solution u or its gradient. For eigenvalue

problems, the coefficients cannot depend on the solution u or its gradient.

But I doubt this will work - usually, c > 0 is required to get acceptable results. Further, "solvepde" is for problems in 2d or 3d - your problem is 1d.

I'm very satisfied with "CLAWPACK" for the solution of hyperbolic PDEs, but it's written in FORTRAN or Python:

https://www.clawpack.org/

[feynman feynman]

I'm interested in 1d through 3d so dimensions are not a problem.

"c > 0 is required to get acceptable results" I want to know this for sure before I decide to use solvepde. Is there further info or worked examples?

What PDE types are solvepde best for?

[Torsten]

"c > 0 is required to get acceptable results" I want to know this for sure before I decide to use solvepde.

I've never seen an example case with c = 0. Such an example would be problematic because for solvepde, you must set boundary conditions on all outer boundaries, but if c = 0, boundary conditions are only physical in "upstream" direction. I'm just a forum member.So if you are not sure whether my information is reliable, you should directly contact support:

https://uk.mathworks.com/support/contact_us.html

Is there further info or worked examples?

https://uk.mathworks.com/products/pde.html

What PDE types are solvepde best for?

The PDE Toolbox (and thus solvepde) is suited to solve elliptic and parabolic partial differential equations in two and three spatial dimensions. It can solve the standard wave equation, but it is not suited to solve general hyperbolic problems of the form du/dt + grad(f(u)) = s.

If you want to test whether the PDE Toolbox fits your needs, you might want to get a trial licence.

[feynman feynman]

thank you. How about periodic boundary conditions for c = 0?

[Torsten]

c = 0 does not work.

Periodic boundary conditions are not implemented - not even for c > 0. I don't know of any commercial software that supports periodic boundary conditions.