Solving PDE using Spectral Method :Solving the Heat Equation with Fourier Transform) (Matlab) 

#FFT #PDE #HeatEquation #Spectral #fouriertransform
إستخدام تحويل فورييه لحل المعادلات التفاضلية الجزئية بالماتلاب
To support: www.paypal.com...
The Fourier transform was originally formulated in the 1800s as a change of coordinates for the heat equation into an eigenfunction coordinate system where the dynamics decouple. More generally, the Fourier transform is useful for transforming partial differential equations (PDEs) into ordinary differential equations (ODEs), Here, we will demonstrate the utility of the FFT to numerically solve a number of PDEs. For an excellent treatment of spectral methods for PDEs, see Trefethen; extensions also exist for stiff
PDEs .