Abstract

MEJIA, Carlos E.. A very useful convolution and some illustrious derivatives. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2019, vol.43, n.168, pp.563-571. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.767.

This paper deals with discrete mollification operators and fractional derivatives. The mollification operators are based on convolutions with truncated Gaussian kernels in one and two dimensions. We begin with a description of their origin and main properties and then we consider two applications that show the usefulness of these operators. Both applications are based on time-fractional diffusion equations. Fractional derivatives deserve to be called illustrious, as we will see later. The first application consists of the stable solution of an inverse problem for a time fractional advection-dispersion equation. The problem consists of the identification of the boundary concentration in a one-dimensional semi-infinite setting. The second application is the stable solution of a problem of source term identification in a bidimensional time-fractional diffusion equation. In each case, we include a description of the problem, the mollification implementation, the method of solution, and some numerical experiments. For the two dimensions problem we include results that were recently published.

Keywords : Convolution; Fractional derivatives; Discrete mollification; Inverse problems.

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )