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MathSource Reviews: Solving the Laplace Equation

Matthew M. Thomas
Organization: Boeing Phantom Works
Journal / Anthology

Mathematica in Education and Resarch
Year: 1998
Volume: 7
Issue: 4
Page range: 67-71

In the previous issue of this journal, we saw how the heat equation in one dimension found a noteworthy application in economics, therein providing a bridge from the physical sciences to their dismal counterpart, and earning Nobel Laureate status for bridge-builders Scholes, Merton, and (posthumously) Black. In this issue, we focus our attention on the physical sciences side of that bridge. We also broaden our perspective beyond a single dimension, and we constrain ourselves to steady state. Our focus is on the 2-D Laplace equation, which is of course the 2-D heat equation at steady state (although its physical meaning goes well beyond heat transfer). We begin by pondering Laplace and his contemporaries, contemplating their accomplishments in the turbulent wake of their time and place in history. We then narrow our scope to the Laplace equation itself, though our narrowed scope blinds us not to the broad physical meaning previously implied. From there, our attention turns to Gennady Stupakov and his contribution to MathSource: A Laplace equation solver for electrostatic problems, given Dirichlet boundary conditions. The Stupakov MathSource items comprise a Mathematica package and a version 3.0 notebook; we will examine both. Finally, our summary will view the strengths and weaknesses of the Stupakov contribution, from what might be described as different sets of eyes.

*Science > Physics > Electromagnetism
*Science > Physics > Thermodynamics and Statistical Mechanics
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Review74.nb (1.2 MB) - Mathematica Notebook