An analytical technique for nonlinear oscillators based on the higher order odd polynomial functions

An analytical technique based on the certain odd polynomial functions is introduced for solving nonlinear oscillatory problems, applicable to both autonomous and non-autonomous cases. A set of algebraic equations are found when the proposed technique is applied. The algebraic equations are linear and relatively straightforward for determining the unknown coefficients associated with the solution. An excellent agreement is found between approximated and numerical solutions, which prove that the technique is very efficient and easy to implement. The technique allows to obtain any desired order of approximate solutions. The results are shown in figures.