One Step Trigonometrically-fitted Third Derivative Method with Oscillatory Solutions

A continuous one step Trigonometrically-fitted Third derivative method whose coefficients depend on the frequency and step size is derived using trigonometric basis function. The method obtained is use to solve standard problems with oscillating solutions. We also discuss the stability properties of the new method . Numerical result obtained via the implementation of the methods shows that the new method performs better than the one step Trigonometrically-fitted second derivative method proposed by Ngwane and Jator [1].