A GOOD INITIAL GUESS FOR APPROXIMATING NONLINEAR OSCILLATORS BY THE HOMOTOPY PERTURBATION METHOD
Ji‐Huan He, Chun‐Hui He, Abdulrahman Ali Alsolami
Abstract
A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess. This article recommends a general approach to construction of the initial guess and the homotopy equation. Duffing oscillator is adopted as an example to elucidate the effectiveness of the method.
Topics & Concepts
Homotopy perturbation methodHomotopy analysis methodDuffing equationMathematicsTrigonometric functionsHomotopyNonlinear systemPerturbation (astronomy)Applied mathematicsMathematical analysisPoincaré–Lindstedt methodn-connectedPure mathematicsPhysicsGeometrySingular perturbationQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsSurfactants and Colloidal Systems