Abstract
We apply the Fourier-least squares method (FLSM) which allows us to find approximate periodic solutions for a very general class of nonlinear differential equations modelling oscillatory phenomena. We illustrate the accuracy of the method by using several significant examples of nonlinear problems including the cubic Duffing oscillator, the Van der Pol oscillator, and the Jerk equations. The results are compared to those obtained by other methods.
Highlights
Oscillatory phenomena are frequently encountered in various fields of science such as, for example, physics, molecular biology, and many branches of engineering
In the present paper we apply the Fourier-least squares method (FLSM) for the computation of approximate periodic solutions for oscillatory phenomena modelled by nonlinear differential equations of the type x(n) (t) = F (x(n−1) (t), x(n−2) (t), . . . , x(1) (t), x (t), t) (1)
In [15], the authors gave a representation of exact solution and approximate solution of Duffing equation involving both integral and nonintegral forcing terms in the reproducing kernel space (RKS)
Summary
Oscillatory phenomena are frequently encountered in various fields of science such as, for example, physics, molecular biology, and many branches of engineering. These oscillatory phenomena can be modelled using nonlinear differential equations. As is known, finding exact solutions of nonlinear differential equations is possible only in some particular cases This justifies the need to resort to approximate methods for the computation of approximate periodic solutions, which in turn could provide important information about the phenomena studied. In the present paper we apply the Fourier-least squares method (FLSM) for the computation of approximate periodic solutions for oscillatory phenomena modelled by nonlinear differential equations of the type x(n) (t) = F (x(n−1) (t) , x(n−2) (t) , . In order to test the accuracy of the method, we apply it to several well-known examples of nonlinear equations and compare the approximate solutions obtained with this method with approximate solutions obtained by other methods
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