论文信息 - The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity

The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity

Abstract In this paper the homotopy perturbation method is adopted for solving a complex-valued second-order strongly nonlinear differential equation. Homotopy with an imbedding parameter p ∈ [ 0 , 1 ] is constructed. The perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex-valued differential equations whose solutions give the approximate solution of the initial differential equation. To illustrate the effectiveness and convenience of the suggested procedure, a Duffing equation with strong cubic nonlinearity is considered. The periodic solution in the first approximation is obtained. The solution is compared with the exact one and shows good agreement.

Livija Cveticanin | L. Cvetićanin

[1] J. Mawhin,et al. Periodic solutions of some complex-valued Liénard and Rayleigh equations , 1999 .

[2] Ji-Huan He. Homotopy perturbation technique , 1999 .

[3] Livija Cveticanin. Approximate analytical solutions to a class of non-linear equations with complex functions , 1992 .

[4] Livija Cveticanin. An asymptotic solution for weak nonlinear vibrations of the rotor , 1993 .

[5] S. Liao. An approximate solution technique not depending on small parameters: A special example , 1995 .

[6] L. Cvetićanin. ANALYTICAL METHODS FOR SOLVING STRONGLY NON-LINEAR DIFFERENTIAL EQUATIONS , 1998 .

[7] HeJi-Huan,et al. Homotopy Perturbation Method , 2003, Advanced Numerical and Semi-Analytical Methods for Differential Equations.

[8] Gamal M. Mahmoud. Approximate solutions of a class of complex nonlinear dynamical systems , 1998 .

[9] Ji-Huan He,et al. Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[10] Ji-Huan He. A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[11] Livija Cveticanin. An approximate solution for a system of two coupled differential equations , 1992 .

[12] P. Byrd,et al. Handbook of Elliptic Integrals for Engineers and Physicists , 2014 .

[13] Livija Cveticanin. Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type , 2001 .