Numerov’s Method for Approximating Solutions to Poisson’s Equation

Matthew S. Norton

 

February 20, 2009

 

 

AbsAAbstract

 

In this paper, a computational approach is taken in trying to solve Poisson’s equa-

tion. Poisson’s equation is often notoriously difficult to solve analytically, so a reliable numerical method has to be established. A Numerov’s sixth order  approximation scheme was used to approximate the solution of Poisson’s equation  for a system in which the analytical solution was known and then compared to see  how much, if any, differences there were between the Numerov approximation and  the analytical solution. After confirming this, Numerov’s method was applied to a situation in which the analytical solution is not known. It was found that the Numerov approximation provides an excellent approximation for the solution of Poisson’s equation.

 

 https://www.siue.edu/~mnorton/Numerov.pdf