COMPUTATIONAL METHODS FOR ONE-DIMENSIONAL FRACTIONAL DIFFUSION EQUATIONS (PREPRINT IBRAE-2002-10)

Preprint IBRAE-2002-09

Goloviznin V.M., Kiselev V.P., Korotkin I.A.

In the work the computing algorithms for the numerical decision of a fractional diffusion primal problem in a one-dimensional case have been developed and analyzed. Fractional diffusion essentially differs from classical diffusion by behavior of substance concentration on large distances from the initial data source. In the publication the review of basic definitions of fractional derivatives is given. On the basis of this definitions difference methods of the first and second orders of approximation have been constructed. Explicit, partially implicit unconditionally stable schemes and a method based on Fourior transform are also given. The numerous examples of calculations represent computing properties of new algorithms, their detailed comparison is carried out, the second order of convergence of the decision of stationary boundary value problem by a method of an establishment is shown. The given algorithms are supposed to be used first of all for the adjustment of methodical questions of an inverse problem decision — estimation of unknown values of fractional diffusion parameters by the results of experiments on location.

Bibliographical reference 

Goloviznin V.M., Kiselev V.P., Korotkin I.A. COMPUTATIONAL METHODS FOR ONE-DIMENSIONAL FRACTIONAL DIFFUSION EQUATIONS. Preprint IBRAE-2002-10. Moscow: Nuclear Safety Institute, May 2002. 35 p. — Refs.: 14 items.