Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1201.35020
Bandrowski, Bartosz; Karczewska, Anna; Rozmej, Piotr
Numerical solutions to integral equations equivalent to differential equations with fractional time. (English)
[J] Int. J. Appl. Math. Comput. Sci. 20, No. 2, 261-269 (2010). ISSN 1641-876X

This paper presents an approximate method of solving a fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. In most of applications related to fractional differential or fractional integro-differential equations, the numerical methods are limited to $1+1$ (time + space) dimensions. This paper presents a different method for solving a fractional integro-differential equation which can handle more dimensional cases within a good approximation. The method is limited to cases when the initial condition is smooth enough with respect to space variables $x$. In such cases the approach works also for $(1+2)$ and $(1+3$) dimensions. More precisely the approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
[Titus Petrila (Cluj-Napoca)]

MSC 2000:: *35A35 Theoretical approximation to solutions of PDE
45D05 Volterra integral equations
65R20 Integral equations (numerical methods)
35R09
35R11

Keywords: Galerkin method; anomalous diffusion

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]