31,652 research outputs found
Numerical solution of fractional Sturm-Liouville equation in integral form
In this paper a fractional differential equation of the Euler-Lagrange /
Sturm-Liouville type is considered. The fractional equation with derivatives of
order in the finite time interval is
transformed to the integral form. Next the numerical scheme is presented. In
the final part of this paper examples of numerical solutions of this equation
are shown. The convergence of the proposed method on the basis of numerical
results is also discussed.Comment: 14 pages, 3 figures, 2 table
Numerical simulations of anomalous diffusion
In this paper we present numerical methods - finite differences and finite
elements - for solution of partial differential equation of fractional order in
time for one-dimensional space. This equation describes anomalous diffusion
which is a phenomenon connected with the interactions within the complex and
non-homogeneous background. In order to consider physical initial-value
conditions we use fractional derivative in the Caputo sense. In numerical
analysis the boundary conditions of first kind are accounted and in the final
part of this paper the result of simulations are presented.Comment: 5 pages, 2 figures, CMM 2003 Conference Gliwice/Wisla Polan
- …