  Classical oscillators of sextic and octic anharmonicities are solved
analytically up to the linear power of \lambda (Anharmonic Constant) by using
Taylor series method. These solutions exhibit the presence of secular terms
which are summed up for all orders. The frequency shifts of the oscillators for
small anharmonic constants are obtained. It is found that the calculated shifts
agree nicely with the available results to-date. The solutions for classical
anharmonic oscillators are used to obtain the solutions corresponding to
quantum anharmonic oscillators by imposing fundamental commutation relations
between position and momentum operators.
