The physically important Burgers' equation is solved using the spectral method
technique with the orthogonal Chebyshev polynomials as its basis functions with some
given boundary conditions. The same problem is again solved utilizing a transformation
method that transforms Burgers' equation to a diffusion equation where the solution to
Burgers' equation is easily found. Nevertheless, the solution to the same problem is found
using a finite difference method. To find the best solution, these three methods are
compared; concluding that numberically the spectral method is highly accurate