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Symbolic PDEs and Eigenfunctions

Devendra Kapadia
Organization: Wolfram Research, Inc.
Department: Kernel Technology

Wolfram Technology Conference 2015
Conference location

Champaign, Illinois USA

The aim of this talk is to give an overview of the new functionality for solving partial differential equations (PDEs) and computing eigensystems of differential operators in Mathematica 10.3. I will begin by using DSolve to find solutions of boundary value problems related to the classical PDEs (wave, heat and Laplace equations), the Schrödinger equation from quantum mechanics, Burgers' equation from fluid mechanics, and the Black-Scholes equation from finance. Next, I will discuss the solution of Sturm-Liouville problems which arise while solving PDEs and in other applications. Finally, I will illustrate the use of DEigensystem for computing eigensystems of ordinary and partial differential operators, which leads to beautiful visualizations of eigenfunctions in two and three dimensions.

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1445534359.nb (4.4 MB) - Mathematica Notebook