Instability of Laplace's Equation
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Initial value problems involving the heat and wave equations enjoy a level of stability that Laplace's equation does not. The solution surface for each of these equations is shown for the initial condition . For close to zero, the initial condition function is close to zero and the entire graphs for both the heat and wave equations are close to zero. The solution to Laplace's equation oscillates wildly, however. This is why boundary conditions, rather than initial conditions, are almost always applied to Laplace's equation.
Contributed by: Mark McClure (March 2011)
Open content licensed under CC BY-NC-SA
"Instability of Laplace's Equation"
Wolfram Demonstrations Project
Published: March 7 2011