pde toolbox in matlab

To use PDE Toolbox in MATLAB, follow the steps below:

1. Open MATLAB.

2. Type "pdetool" in the command window and press Enter. This will open the PDE Toolbox.

3. In the PDE Toolbox, you can create a new model or open an existing model.

4. To create a new model, go to File -> New Model.

5. In the New Model dialog box, enter a name for the model and select the geometry type (such as rectangle or circle). Then click OK.

6. The PDE Toolbox will open a new window containing the geometry of the model.

7. To define the physics of the problem, click on the Physics tab in the PDE Toolbox window. Here, you can select the type of problem (such as elliptic or parabolic) and choose the coefficients for the partial differential equation.

8. Once you have defined the geometry and physics of the model, you can solve it by clicking on the Solve button in the PDE Toolbox window.

9. MATLAB will solve the PDE and display the results in a new window.

main.m
% Example usage of PDE Toolbox
% Create a new model with a circular geometry and solve Poisson equation
% on the unit circle with zero boundary condition

% Define the geometry
model = createpde();
geometryFromEdges(model,@circleg);

% Define the problem
specifyCoefficients(model,'m',0,'d',0,'c',1,'a',0,'f',0);
setBoundaryCondition(model,'dirichlet','Edge',1:model.Geometry.NumEdges,'u',0);

% Solve the problem
generateMesh(model);
result = solvepde(model);

% Visualize the solution
pdeplot(model,'XYData',result.NodalSolution)
title('Solution to Poisson equation on a unit circle')
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