A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method

This paper deals with the diffusion transport equation in one dimensional space. The B-spline Galerkin approximation method together with the Fourier transform and Gauss–Hermite quadrature are proposed to compute approximate solution. We give some theoretical results such as existence and uniqueness of the solution and an upper error bound estimates. We also give some numerical examples to illustrate the effectiveness of a such method.