Assessment of Homotopy Analysis Method and Modified Homotopy Perturbation Method for Strongly Nonlinear Oscillator

Some recently developed analytical methods namely; homotopy analysis method, homotopy per- turbation method and modified homotopy perturbation method are applied successfully for solving strongly nonlinear oscillators. The analytical results obtained by using HAM are compared with those of HPM, mH- PM as well as with numerical results. In this study, different examples with strong nonlinearity are assessed in detail to illustrate the effectiveness and convenience of the methods. Comparing the three methods, the attention is focused on the accuracy of the results and applicability of the methods. It has been observed that the solution using HAM which is valid in a small region is more accurate than the solutions obtained using other two methods. Whereas mHPM works very well for a wide range and it is computationally more efficient.