The Wave Equation

The PDE that defines the wave equation falls under the class of Hyperbolic partial differential equations.  The equation is:

 

 

 
This 2^nd order PDE with the boundary value conditions can be numerically solved by first converting it into two 1^st order PDE’s, described by:

 

 

 

The two PDE’s can then be converted into ODE’s using the Method of Lines:

 

 

By dividing the spatial domain into N elements over the total length L, the 2^nd order PDE has now reduced to a set of ODE’s that can be quite easily integrated numerically.