Changes between Version 15 and Version 16 of u/erica/PoissonSolver

Timestamp:

08/19/13 12:52:06 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/PoissonSolver

@@ -25 +25 @@
 The solutions to both Poisson's and Laplace's equations satisfy the Uniqueness theorem (see Griffith's E&M textbook). That is, if the solution satisfies the aforementioned 2 conditions, it is the ''unique'' solution to the equation. 
 
-As is, Poisson's equation is set up to solve for f (be it charge density, or matter density, etc.) given some potential (e.g. electrical or gravitational, etc.). However, in most situations we have the opposite information about a system -- given the density, we seek the potential. This requires some numerical techniques to solving this 2nd order differential equation, especially for those systems that do not admit closed-form expressions.
+As is, Poisson's equation is set up to solve for f (be it charge density, or matter density, etc.) given some potential (e.g. electrical or gravitational, etc.). However, in most situations we have the opposite information about a system -- given the density, we seek the potential. This requires some numerical techniques for solving this 2nd order differential equation, especially for those systems that do not admit closed-form solutions.
 
 = Equation Discretization =