Abstract:
Partial differential equations P.D.Es govern mechanical systems which
contain multiple parameters. Linear and certain non-linear P.D.Es can
be solved using such analytic methods as separation of variables. How-
ever, certain P.D.Es exist, which cannot be solved analytically. This
calls for an alternative method of solution. Finite difference Methods
(F.D.Ms) provide a realistic physical approach towards the modeling of
these problems. The wave equation can be solved using the explicit and
therefore conditionally stable Forward in Time and Centered in Space
F.T.C.S F.D.M. It is shown here that the Local Truncation Error (LTE)
in the result is relatively negligible. An implicit scheme, which is uncon-
ditionally stable, is developed and the conclusion made that the scheme
can be used to solve other non-linear P.D.Es with a higher degree of
stability.
