ABSTRACT
This chapter presents numerical methods for solution of partial differential equations (PDE), in particular, those that describe some fundamental problems in engineering applications, including Laplace's equation, the heat equation, and the wave equation. The user-defined function Dirichlet PDE uses the difference-equation approach outlined above to numerically solve Poisson's equation or Laplace's equation in a rectangular region with the values of the unknown solution available on the boundary. The user-defined function Peaceman Rachford alternating direction implicit (PRADI) uses the PRADI method to numerically solve Poisson's equation Laplace's equation in a rectangular region with the values of the unknown solution available on the boundary. The user-defined function Heat1DFD uses the finite-difference approach to solve the one-dimensional heat equation subject to zero boundary conditions and a prescribed initial condition. The chapter also presents two techniques for the numerical solution of parabolic PDEs: the finite-difference method and Crank Nicolson method.
