Laplace's equation

Boundary value problem

Applied mathematics

Soundness

Vibration

Computer science

Acoustics

Fractional Fourier transform

Physics

Mathematics

Laplace transform

Inverse Laplace transform

Fourier analysis

Two-sided Laplace transform

Mathematical analysis

Programming language

Laplace transform applied to differential equations

Fourier transform

Acta Mechanica et Automatica

In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform. Here, we present a comparative study of the new technique based on Laplace transform and the previous techniques of maximum minimum approach (MMA) and amplitude frequency formulation (AFF) for the analytical results. For the non-linear oscillators, MMA, AFF and VIM by Laplace transform give the same analytical results. Comparison of analytical results of VIM by Laplace transform with numerical results by fourth-order Runge–Kutta (RK) method conforms the soundness of the method for solving non-linear oscillators as well as for the time and boundary conditions of the non-linear oscillators.

Modified Laplace Based Variational Iteration Method for the Mechanical Vibrations and its Applications