Authors : H. Arabshahi
Abstract: A new numerical method has been carried out to solve the differential equation using Fast Fourier Transform (FFT). The new algorithm has been accompanied by a numerical example. Firstly, we solve a Cauchy problem for an elastic vibrating system using the finite difference method. Then with the values of the approximate solution obtained in the equidistant points from the interval (0, 1), we shall find an interpolation polynomial using FFT. Also we study, the approximation of the numerical solution and stability of the difference scheme which correspond of a second-order differential equation.
H. Arabshahi , 2011. A New Method for Solutions of Differential Equation by Fast Fourier Transform. Journal of Modern Mathematics and Statistics, 5: 21-24.