Numerical Analysis of Nonlinear Partial Differential Equations by Fourier Spectral Method

The Fourier spectral method which uses the Fourier transform and the Fourier inverse transform are applied to the nonlinear and linear partial differential equations. The partial differential equation becomes the ordinary differential equation after the Fouier transform used and it is solved by the Runge-Kutta method. The solutions of linear Burgers' equation are carefully checked by being compared with the analytical solutions and this method was applied to nonlinear Burgers' equation. The initial conditions are cos x, sin x and Gaussian distribution.