Maplesoft

Diffusion with a Generalized Robin Condition

The one-dimensonal heat equation with a generalized Robin condition is solved on [0, 1] by a finite-difference scheme and by the Laplace transform, with the inversion implemented numerically. The left end is insulated and the initial temperature is zero. The Robin condition at the right end is driven by a function governed by an ODE, that is in turn, driven by the endpoint temperature. Hence, this webinar shows how to discretize this coupled PDE/ODE, and how to approximate the solution with Laplace transforms. The inversion of the resulting transforms requires numerical techniques, so we illustrate evaluation of the Bromwich inversion integral numerically. We also illustrate Maple's functionality for numerically inverting Laplace transforms.
Language: English
Duration: 45 Minutes
Related Terms: Ode, Laplace, Laplace-transform