Fourier transform is applied to remove the time-dependent variable in the
diffusion equation. Under non-harmonic initial conditions this gives rise to a
non-homogeneous Helmholtz equation, which is solved by the method of
fundamental solutions and the method of particular solutions. The particular
solution of Helmholtz equation is available as shown in [4, 15].
The approximate solution in frequency domain is then inverted
numerically using the inverse Fourier transform algorithm. Complex frequencies
are used in order to avoid aliasing phenomena and to allow the computation of
the static response. Two numerical examples are given to illustrate the
effectiveness of the proposed approach for solving 2-D diffusion equations.