The idea of employing the discrete Fourier transform casted as the representative cell method for the solution of multiscale problems is illustrated. Its application in combination with analytical (structural mechanics methods, Wiener-Hopf method, integral transform methods) and numerical (finite element method, higher-order theory) methods is demonstrated. Both cases of 1-D and 2-D translation...

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

Our purpose in this study was to present an integral-transform approach to the analytical solutions of the Pennes' bioheat transfer equation and to apply it to the calculation of temperature distribution in tissues in hyperthermia with magnetic nanoparticles (magnetic hyperthermia). The validity of our method was investigated by comparison with the analytical solutions obtained by the Green's f...