Gamma function method for the nonlinear cubic-quintic Duffing oscillators
Kang‐Jia Wang, Guo‐Dong Wang
Abstract
In this article, the gamma function method, for the first time ever, is used to solve the nonlinear cubic-quintic Duffing oscillators. The nonlinear cubic-quintic Duffing oscillators with and without the damped and quadratic terms are considered respectively. By the gamma function method, it only needs one-step to get the approximate solution. The comparisons with the existing solutions reveal that the proposed method is simple but effective in solving the small amplitude oscillation.
Topics & Concepts
Quintic functionDuffing equationCubic functionQuadratic equationSimple (philosophy)Nonlinear systemFunction (biology)MathematicsMathematical analysisOscillation (cell signaling)AmplitudeCubic crystal systemApplied mathematicsPhysicsQuantum mechanicsGeometryCondensed matter physicsPhilosophyBiologyGeneticsEvolutionary biologyEpistemologyFractional Differential Equations SolutionsComposite Structure Analysis and OptimizationIterative Methods for Nonlinear Equations