How to solve a Partial Differential Ecuation?

I am a very new person using matlab, I want to know how to solve a PDE such as using matlab software. In addition, it will be very usefull if you can also told me how to solve it as a part of a Cauchy's problem with an initial condition or with some boundary conditions.

Thank you.

Answer 1

[Torsten]

The code at the end of the link solves a single equation.

MATLAB does not have the ability to symbolically solve PDEs. If you write down the ODEs for your problem that come from the method of characteristics, you might succeed using MATLAB's "dsolve".

The equations are

du/ds = u
dx/ds = x+x^2
dt/ds = 1

with u = u(x(s),t(s))

You will have to define your boundary conditions to get a unique solution.

Best wishes

Torsten.

Answer 2

[Torsten]

Here is code to start from:

https://de.mathworks.com/matlabcentral/answers/440015-first-order-partial-differential-equations-system-numerical-solution

Best wishes

Torsten.

[José Luis Lavado Sánchez]

But this for solving a sistem of equations no? I want to know how to solve only one equation. And also I think the link is about a numerical solution and I am searching for a symbolic solution.