Abstract:
In this work, a class of Continuous Trigonometrically-Fitted Methods (CTFMs) for the solution
of second order oscillatory Ordinary Differential Equations (ODEs) is considered. To
develop the CTFMs, the assumed approximate solution from the basis function for the problem
are interpolated at some selected grid points while collocation of the differential system
arising from the basis function was done at all grid points. The coefficients of the methods
developed depend on the frequency of the oscillatory component of each the continuous
methods. This frequency is a function of the stepsize of the methods. The unknown parameters
in the system of linear equations arising from the collocation and interpolation
functions were determined and the values substituted in the approximate solution to the
problem. The result was simplified to obtained each of the required continuous methods.
Discrete Trigonometrically-Fitted Methods (DTFMs) were recovered from the CTFMs as a
by product. Stability and other properties of the discrete methods were examined to confirm
the accuracy and usability of the methods.The new methods were applied to solve linear
and non-linear oscillatory problems in ODEs. The results were found to be better in accuracy
than any of the methods considered in literature that solved the same problems.
