Numerical solutions to integral equations equivalent to differential equations with fractional time

Authors:
Bartosz Bandrowski;Anna Karczewska;Piotr Rozmej
Affiliations:
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland;Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland;Institute of Physics, University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland
Venue:
International Journal of Applied Mathematics and Computer Science
Year:
2010

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Abstract

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. 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.