The three level two point scheme for the vibrating membrane problem

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.