Put your problem in the correct form for Partial Differential Equation Toolbox™ solvers. For details, see Equations You Can Solve Using Partial Differential Equation 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 Visualization.