An Accurate Analytical Solution to Strongly Nonlinear Differential ...

The NHBM is one of the most efficient methods for obtaining analytical approximate solutions for strongly nonlinear differential equations. It ...

"An Accurate Analytical Solution to Strongly Nonlinear Differential ...

The study presents an alternative analytical method called Newton Harmonic Balance Method (NHBM) to provide an analytical solution for two nonlinear ...

Abstract. Abstract: The study presents an alternative analytical method called Newton Harmonic Balance Method (NHBM) to provide an analytical solution for two ...

01-Applied Mathematics & Information Sciences

An Accurate Analytical Solution to Strongly Nonlinear Differential Equations. PP: 141-149. doi:10.18576/amis/140118. Author(s).

Analytical technique for solving strongly nonlinear oscillator ...

The advantage of using the Gamma function method (GFM) is that it provides analytical solutions to nonlinear differential equations directly, ...

Strong Nonlinear Oscillators: Analytical Solutions - SpringerLink

This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong ...

A new reliable analytical solution for strongly nonlinear oscillator ...

On the contrary, the techniques of solutions of nonlinear differential equations (NDEs) are less available and have no exact solution and, in general, linear ...

(PDF) Analytical approximate technique for strongly nonlinear ...

The most significant features of this method are its simplicity and excellent accuracy for the whole range of oscillation amplitude values. Also ...

Highly accurate analytical solution for free vibrations of strongly ...

Indeed, it is found that our proposed technique produces more accurate and computationally results than the rival known methods. The obtained ...

Accurate analytical solution of the circular sector oscillation by the ...

Perturbation methods were the first analytical and approximate methods to achieve approximate analytical solutions for nonlinear differential ...

Highly accurate analytical solution for free vibrations of strongly ...

... show the efficiency and capability of the present perturbation technique to be applied to various strongly nonlinear differential equations.

Analytical solution of strongly nonlinear Duffing oscillators - Scipedia

To show the remarkable accuracy of the obtained result, the approximate solution with the energy balance method [18], homotopy perturbation ...

Construction of approximate analytical solutions to strongly ...

Only a few iterations can provide very accurate approximate analytical solutions even if the nonlinearity and damping are significant.

Accurate analytical solutions to nonlinear oscillators by means of the ...

A trial solution is selected with unknown parameters. Next, the Ritz–He method is used to obtain the unknown parameters. This will yield the ...

Accurate Approximate Analytical Solution of Nonlinear Oscillators

A more accurate approximate analytical solution of nonlinear oscillator has been provided by using modified energy balance method.

Analytical and Approximate Solutions to the Fee Vibration of ...

Most of real systems are modeled by nonlinear differential equations which are important issues in mechanical structures, mathematical physics and engineering.

(Open Access) Analytical solution of strongly nonlinear Duffing ...

... accurate analytical solution for nonlinear differential equation with inertia and static nonlinearity. ...read more read less. 14. •Journal Article•DOI ...

(PDF) Highly accurate analytical solution for free vibrations of ...

The Duffing oscillator (damped or undamped) is one of the most significant and classical nonlinear ordinary differential equations in view of its diverse ...

A new reliable analytical solution for strongly nonlinear oscillator ...

List of references · Elmas, A new perturbation technique in solution of nonlinear differential equations by using variable transformation, Appl Math Comp, № 227, ...

Accurate analytical solutions for nonlinear oscillators with ...

In this study, three approximate analytical methods have been proposed to prepare an accurate analytical solution for nonlinear oscillators with fractional ...