Dr. Robert Lopez

Maple-Based Numeric-Symbolic Techniques for PDE BVPs

Maple provides analytic solutions to many Boundary Value Problems for elliptic, parabolic, and hyperbolic partial differential equations. The evolution equations (parabolic and hyperbolic) can be in one or more spatial dimensions. When it comes to numeric solutions, Maple's built-in numeric solver handles evolution equations in one spatial dimension only, but in this webinar, I will present techniques that can be used to find solutions in two spatial dimensions.

In 2014, Dr. Sam Dao, then an Application Engineer with Maplesoft, presented the webinar Handling Partial Differential Equations. In it, he demonstrated numeric-symbolic techniques for solving a parabolic BVP in one spatial dimension. The techniques were finite difference, Galerkin, and collocation, each infused with a touch of the Method of Lines.

Intrigued by the use of MoL in these techniques, I decided to take a closer look at Dr. Dao's work with the intention of extending his approach to equations in two spatial dimensions. The result is the present webinar where finite difference, Rayleigh-Ritz, Galerkin, and collocation techniques are illustrated, and extended to equations in two spatial dimensions.
Language: English
Duration: 51 Minutes
Related Terms: Bvp, Differential-equations, Hyperbolic, Elliptic, Parabolic