Stability (learning theory)

Combinatorics

Physics

Nonlinear system

Perturbation (astronomy)

Pure mathematics

Theology

Mathematics

Homotopy perturbation method

Gene

Duffing equation

Machine learning

Rank (graph theory)

Mathematical analysis

Philosophy

Homotopy analysis method

Chemistry

Transformation (genetics)

Third order

Computer science

Quantum mechanics

Applied mathematics

Biochemistry

Homotopy

Numerical Methods for Partial Differential Equations

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.

The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation