PDE toolbox c coefficient

*Hi I have two PDE equations and I want to solve them using Matlab PDE and I don't know how to find C because it is very confusing. The equations are as follows.

(∂^2 ψ)/(∂^2 x)=(∂Q_x)/∂x

(∂^2 ψ)/(∂^2 y)=(∂Q_y)/∂y*

Answer 1

[Alan Weiss]

Your equations are not a form that fits into PDE Toolbox framework.

In fact, they seem strange to me in any case. The first equation can be integrated to give

(∂ ψ)/(∂ x)=(Q_x) + K, where K is a constant of integration

Similarly,

(∂ ψ)/(∂ y)=(Q_y) + K2.

So it seems that you can find ψ by integrating Q_x or Q_y. However, it seems that this integration will likely lead to inconsistencies, unless Q_x and Q_y have very particular forms. Imagine integrating over x first then y, or y first then x. You might arrive at two different values for ψ.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kaveh Gharibi]

Alan,

Thank you! I understand what you are saying , but even if it is wrong can I use PDE toolbox to solve it?

[Alan Weiss]

As I already said, your equation is not in a form that PDE Toolbox can handle. Indeed, I recommend that you double-check to make sure that you have a correct equation. If the equation is correct then I suggest that you solve it by integrating Q_x and Q_y, including constants of integration that are appropriate for your boundary conditions.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kaveh Gharibi]

Alan,

Thank you very much!

Kaveh