On Exact Discretization Technique for the Solution of Oscillatory Problems of Third Order

One of the techniques needed to construct an efficient method for the solution of oscillatory problems is exact discretization. This technique is adopted in the construction of a new Exact Finite Difference Scheme (EFDS) for the solution of third order oscillatory problems. In carrying out the construction of the method, it was assumed that at any point within the interval of integration, the approximate/numerical solution coincides with the exact/theoretical solution. The analysis of the method was also carried out to show that third order oscillatory problems that possess solutions also have their corresponding EFDS. The method derived was then applied on some modeled third order oscillatory problems and from the results obtained, it is obvious that the EFDS derived did not exhibit any numerical instabilities. As a matter of fact, the computed solutions of the EFDS are exactly equal to the exact solutions.