A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform (Advances in Applied Mathematics and Mechanics, 2011)
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 offundamental solutions and the method of particular solutions. The particularsolution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then invertednumerically using the inverse Fourier transform algorithm. Complex frequenciesare used in order to avoid aliasing phenomena and to allow the computation ofthe static response. Two numerical examples are given to illustrate theeffectiveness of the proposed approach for solving 2-D diffusion equations.