Solution of the ENSO Delayed Oscillator with Homotopy Analysis Method

An ENSO delayed oscillator is considered. The El Nino atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. Using the homotopy analysis method, the approximate expansions of the solution of corresponding problem are constructed. The method is based on a continuous variation from an initial trial to the exact solution. A Maclaurin series expansion provides a successive approximation of the solution through repeated application of a differential operator with the initial trial as the first term. This approach does not require the use of perturbation parameters and the solution series converges rapidly with the number of terms. Comparing the approximate analytical solution by homotopy analysis method with the exact solution, we can find that the homotopy analysis method is valid for solving the strong nonlinear ENSO delayed oscillator model.