Application of fast fourier transformation in numerical solution of differential equations

In this expository paper, we will be looking at different concepts of Fast Fourier transform. In this we see that how the Fast Fourier Transform behaves. FFT is the fast algorithm. Here we will look at the different examples. Fast Fourier Transform has long been set up as a necessary tool in signal processing. FFT is used in many fields which are mainly used to visualize signals. In this paper, we take one example of second order elliptic partial differential equation. In this example, we have obtained the Fourier coefficients of the solution, without needing to solve linear algebraic equations. In this we also discuss about DFT. DFT converts a finite sequence of equally spaced samples of a function into a same length sequence of equally spaced samples of the discrete time Fourier Transform, which is a complex-valued function of frequency. In this paper, we also discuss some of the important applications of FFT.