Displaying similar documents to “A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.”

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

Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)

International Journal of Applied Mathematics and Computer Science

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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.

Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems

Béla J. Szekeres, Ferenc Izsák (2017)

Applications of Mathematics

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Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on ℝ 2 and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the...

A finite difference method for fractional diffusion equations with Neumann boundary conditions

Béla J. Szekeres, Ferenc Izsák (2015)

Open Mathematics

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A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. The basis of the mathematical model and the numerical approximation is an appropriate extension of the initial values, which incorporates homogeneous Dirichlet or Neumann type boundary conditions. The wellposedness of the obtained initial value problem is proved and it is pointed out that each extension is compatible with the original boundary conditions. Accordingly,...

Optimal approximation simulation and analog realization of the fundamental fractional order transfer function

Abdelbaki Djouambi, Abdelfatah Charef, Alina Voda besancon (2007)

International Journal of Applied Mathematics and Computer Science

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This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase...

Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał Stanisławski, Krzysztof J. Latawiec (2012)

International Journal of Applied Mathematics and Computer Science

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This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated...