Documentation

Put your problem in the correct form for Partial Differential Equation Toolbox™ solvers. For details, see Equations You Can Solve Using PDE Toolbox. If you need to convert your problem to divergence form, see Put Equations in Divergence Form.

Create a PDEModel model container. For scalar PDEs, use createpde with no arguments.

model = createpde();

If N is the number of equations in your system, use createpde with input argument N.

model = createpde(N);

Import or create the geometry. For details, see Geometry and Mesh.

importGeometry(model,'geometry.stl'); % importGeometry for 3-D
geometryFromEdges(model,g); % geometryFromEdges for 2-D

View the geometry so that you know the labels of the boundaries.

pdegplot(model,'FaceLabels','on') % 'FaceLabels' for 3-D
pdegplot(model,'EdgeLabels','on') % 'EdgeLabels' for 2-D

To see labels of a 3-D model, you might need to rotate the model, or make it transparent, or zoom in on it. See STL File Import.

Create the boundary conditions. For details, see Specify Boundary Conditions.

% 'face' for 3-D
applyBoundaryCondition(model,'dirichlet','face',[2,3,5],'u',[0,0]);
% 'edge' for 2-D
applyBoundaryCondition(model,'neumann','edge',[1,4],'g',1,'q',eye(2));

Create the PDE coefficients.

f = [1;2];
a = 0;
c = [1;3;5];
specifyCoefficients(model,'m',0,'d',0,'c',c,'a',a,'f',f);

For time-dependent equations, or optionally for nonlinear stationary equations, create an initial condition. See Set Initial Conditions.

Create the mesh.

generateMesh(model);

Call the appropriate solver. For all problems except for eigenvalue problems, call solvepde.

result = solvepde(model); % for stationary problems
result = solvepde(model,tlist); % for time-dependent problems

For eigenvalue problems, use solvepdeeig:

result = solvepdeeig(model);

Examine the solution. See Solution and Gradient Plots with pdeplot and pdeplot3D, 2-D Solution and Gradient Plots with MATLAB® Functions, and 3-D Solution and Gradient Plots with MATLAB® Functions.