ABSTRACT
The programmatic tool of the PDE Toolbox is presented. Finite element numerical solutions are explained by the collocation method for an elliptic PDE of second order. The minimum required set of PDE Toolbox commands for the step-by-step solution of elliptic, parabolic, hyperbolic, and eigenvalue PDEs with Dirichlet and/or Neumann boundary conditions is presented. PDE solutions are explained step-by-step. The created programs solve PDEs for various engineering problems, including Poisson’s equation (electrostatics) for a square plate with a rectangular slot, an eigenvalue equation for a square membrane, and an equation of unsteady heat transfer for a small aluminum plate as well as a wave equation for a drum and an eigenvalue equation for elliptical membrane.
