Explicit Methods For Wave Equations

Explicit Method :   Explicit method is used in numerical analysis for determining the time dependent ordinary and partial differentiation.

 

Derivation :

Using central differences, we write the approximations

 

......................1.1

........................1.2

 

Applying the differential equation at the nodal point (x_i , t_j), and using the central difference approximations, (1.2), (1.2), we get

 

or,

......................1.3

 

where r = kc/h, is called the mesh ratio parameter.

Figure : Nodes in explicit method