MATLAB: Partial Differential Equation Toolbox

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Help please, I need to solve this differential equation

in Matlab (where "a" is a constant parameter, it can be taken by any), I wanted to use the Partial Differential Equation Toolbox, but I ran into a problem, the elliptic equation in this Toolbox is represented in a vector form, namely -div(c*grad(u))+a*u=f.

Please help me convert my equation to this form and tell me how it can be done or at least name the sources of information from which I can learn this knowledge.

I really need to solve this equation in Matlab,so please tell me how it can be done.

Best Answer

Take

c = [- x, x - y ; - ( x - y ), - y]

Then

-div(c*grad(u)) = x * d^2u/dx^2 + y * d^2u/dy^2

Section 2-62 in

http://www.cmap.polytechnique.fr/~jingrebeccali/frenchvietnammaster2_files/2017/pdetool_doc

Related Solutions

MATLAB: Numerical Solution for a System of THREE Differential Equations

This is an ODE, not PDE. Look for the ODE suite

MATLAB: How do assign the variables f1 and f2 for a nonlinear system PDE using PDETOOL

Before solving the PDE, select "Parameters ..." from the Solve menu and check the "Use nonlinear solver" option. The solution to the 1st PDE is referenced as u(1,:) and the solution to the 2nd PDE is referenced as u(2,:). Now you can set the coefficients f1 and f2 in the GUI. In your example:

f1=sinh(u(1,:))
f2=sinh(u(1,:))

For more information about the Non-Linear Equations, please refer to pages 1-21 and 4-21 to 4-25 of the "Partial Differential Equation Toolbox" documentation. This documentation can also be found online at the following URL:

https://www.mathworks.com/help/pdf_doc/pde/pde.pdf

Best Answer

Related Solutions

MATLAB: Numerical Solution for a System of THREE Differential Equations

MATLAB: How do assign the variables f1 and f2 for a nonlinear system PDE using PDETOOL

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