The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation
Ji‐Huan He, Yusry O. El‐Dib
Abstract
Abstract In the current work, we apply a nonstandard scheme to solve the third‐order Duffing equation. This equation is produced from the strong damped Klein–Gordon equation under the traveling wave transformation. The solution and the stability conditions for the third‐order Duffing equation have been discussed for the first time. The present analysis is new and used the reducing rank method with the homotopy perturbation method. A nonoscillator solution with the oscillating solutions is derived individually and frequency formula is obtained. Besides, the stability analysis is discussed.
Topics & Concepts
MathematicsDuffing equationHomotopy perturbation methodHomotopy analysis methodMathematical analysisPerturbation (astronomy)Third orderStability (learning theory)Transformation (genetics)Applied mathematicsHomotopyRank (graph theory)Nonlinear systemPure mathematicsPhysicsCombinatoricsBiochemistryPhilosophyChemistryMachine learningQuantum mechanicsComputer scienceTheologyGeneFractional Differential Equations SolutionsNonlinear Waves and Solitons