Homotopy perturbation method with three expansions
Copyright policy )Homotopy perturbation method with three expansions
The authors suggest the homotopy perturbation method with three expansions to solve nonlinear oscillator problems with damping terms. They solve the Duffing equation with linear damping to explain the homotopy method with three expansions. In addition to the homotopy perturbation method they add the amplitude expanding method. The solutions obtained by the homotopy method with three expansions are in good agreement with the analytical solutions. The influence of the damping is also shown. Finally the work is illustrated by a numerical example and the comparison with analytical solutions.
- Soochow University China (People's Republic of)
- Henan Polytechnic University China (People's Republic of)
- Ain Shams University Egypt
- Xi'an University of Architecture and Technology China (People's Republic of)
exponential decay parameter, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Nonlinear oscillations and coupled oscillators for ordinary differential equations, homotopy perturbations method, damping Duffing equation, Theoretical approximation of solutions to ordinary differential equations
exponential decay parameter, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Nonlinear oscillations and coupled oscillators for ordinary differential equations, homotopy perturbations method, damping Duffing equation, Theoretical approximation of solutions to ordinary differential equations
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