Modifying DTM to solve nonlinear oscillatory dynamics

The lack of DTM in oscillatory dynamics will be cured using the Sin and Cos After Treatment (SAT and CAT). The use of Direct Transformation Method (DTM) to solvelinear and nonlinear differential equations will be given first. The DTM outcome is equated with the Taylor series. For even and odd powers terms expressions incorporating the Cosand Sin functions are respectively used. For highly nonlinear dynamics when both odd andeven powers are in presence, both trigonometric functions simultaneously are suggested to be used. Some examples are given to show the details and the effectiveness of the suggestion

Keywords:

Taylor series , DTM , trigonometric function , oscillatory dynamics , CAT and SAT DTM