New iterative technique for computing Fourier transforms.

Abstract

The Fourier transformations have stimulated many amounts of articles in recent years. they arise in the fields of engineering, control systems, and technology like analyzing signals in electronic circuits, radio circuits, cell phones, image processing, and in solutions to heat transfer equations, Airy equations, Telegraph equations, Duffing equations, Wave equations, Fisher equations, Laplace equation, etc. In this paper, a new iterative method called Adomian Decomposition Method (ADM) is implemented to obtain the Fourier transform of functions by solving a linear ordinary differential equation of first order. This method focuses on finding Fourier transforms by knowing the series resulting from Adomian polynomials. Five famous examples are presented to test the effectiveness and validity of this technique. The results indicate that the accuracy of this method is fully in agreement with the classical method. Furthermore, when applying the Adomian decomposition method, we noticed that it provides accurate results and does not require a lot of time and effort to obtain Fourier transforms of the functions because it does not require a large number of iterations.

Keywords

• ordinary differential equations
• adomian decomposition method
• fourier transform