Relaxation Technique for Solving Laplace's Equation

Highlights of the activity

1. This small group activity is designed to teach students to solve Laplace's equation using any given set of boundary conditions.
2. Students use a technique of successive approximations to find the solution (similar to many numerical strategies).
3. The whole class discussion focuses on comparing the relaxation strategy to other familiar methods of solving Laplace's equation.

Reasons to spend class time on the activity

Students in the middle division typically have little experience solving differential equations and few students have experience using numerical methods for doing so. This activity introduces students to a relaxation strategy for solving a homogeneous second-order differential equation (Laplace's Equation).

Reflections

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Instructor's Guide

• Wiki version