Abstract:
In this research work the novel optimal central finite difference schemes for solving
the transient wave equation, are developed and analyzed. The novel schemes (a)
give exact value at the nodes of the grid, meaning that an exact solution is possible
for the transient wave equation; (b) the key advantage is that they have the simple
structure as that of the standard central finite difference schemes, so we just need
to make few amendments in the standard codes, instead of writing the new codes
altogether; (c) above all, the beauty lies in the fact that they do not require fine
mesh size and works for any wave number, specially for high wave number. Finally,
in order to display the actual power of the novel schemes, numerical computations
and graphical representations for two model problems are added, by using both
novel and standard central finite difference schemes, which support our theoretical
results, by showing the superiority of the novel schemes compared to the standard
schemes.
