## Search

Now showing items 31-33 of 33

JavaScript is disabled for your browser. Some features of this site may not work without it.

All of ChesterRepCommunitiesTitleAuthorsPublication DateSubmit DateSubjectsPublisherJournalThis CommunityTitleAuthorsPublication DateSubmit DateSubjectsPublisherJournal

SubjectsError estimates (9)error estimates (6)Caputo fractional derivative (4)Finite difference method (4)stability (4)finite element method (3)Laplace transform (3)numerical schemes (3)Caputo derivative (2)discrete equations (2)View MoreJournalJournal of Computational and Applied Mathematics (4)Computational Methods in Applied Mathematics (3)Applied Numerical Mathematics (2)Fractional Calculus and Applied Analysis (2)Journal of Computational Physics (2)View MoreAuthors

Yan, Yubin (33)

Ford, Neville J. (11)Khan, Monzorul (4)Liang, Zongqi (4)Liu, Fang (4)Pal, Kamal (4)Li, Zhiqiang (3)Xiao, Jingyu (3)Liu, Yanmei (2)Malique, Md A. (2)View MoreTypesArticle (30)Book chapter (2)Meetings and Proceedings (1)

Now showing items 31-33 of 33

- List view
- Grid view
- Sort Options:
- Relevance
- Title Asc
- Title Desc
- Issue Date Asc
- Issue Date Desc
- Results Per Page:
- 5
- 10
- 20
- 40
- 60
- 80
- 100

On the behavior of the solutions for linear autonomous mixed type difference equation

Yan, Yubin; Yenicerioglu, Ali Fuat; Pinelas, Sandra

A class of linear autonomous mixed type difference equations is considered, and some new
results on the asymptotic behavior and the stability are given, via a positive root of the
corresponding characteristic equation.

Numerical methods for solving space fractional partial differential equations by using Hadamard finite-part integral approach

Yan, Yubin; Wang, Yanyong; Hu, Ye

We introduce a novel numerical method for solving two-sided space fractional partial differential equation in two dimensional case. The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order $O(h^{3- \alpha})$, where $h$ is the space step size and $\alpha\in (1, 2)$ is the order of Riemann-Liouville fractional derivative. Based on this scheme, we introduce a shifted finite difference method for solving space fractional partial differential equation. We obtained the error estimates with the convergence orders $O(\tau +h^{3-\alpha}+ h^{\beta})$, where $\tau$ is the time step size and $\beta >0$ is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation. Unlike the numerical methods for solving space fractional partial differential equation constructed by using the standard shifted Gr\"unwald-Letnikov formula or higher order Lubich'e methods which require the solution of the equation satisfies the homogeneous Dirichlet boundary condition in order to get the first order convergence, the numerical method for solving space fractional partial differential equation constructed by using Hadamard finite-part integral approach does not require the solution of the equation satisfies the Dirichlet homogeneous boundary condition. Numerical results show that the experimentally determined convergence order obtained by using the Hadamard finite-part integral approach for solving space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained by using the numerical methods constructed with the standard shifted Gr\"unwald-Letnikov formula or Lubich's higer order approximation schemes.

Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises

Liu, Fang; Yan, Yubin; Khan, Monzorul (EudoxusPress, 2018-02-28)

Fourier spectral methods for solving stochastic space fractional partial differential equations driven by special additive noises in one-dimensional case are introduced and analyzed. The space fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject to some boundary conditions. The space-time noise is approximated by the piecewise constant functions in the time direction and by some appropriate approximations in the space direction. The approximated stochastic space fractional partial differential equations are then solved by using Fourier spectral methods. For the linear problem, we obtain the precise error estimates in the $L_{2}$ norm and find the relations between the error bounds and the fractional powers. For the nonlinear problem, we introduce the numerical algorithms and MATLAB codes based on the FFT transforms. Our numerical algorithms can be adapted easily to solve other stochastic space fractional partial differential equations with multiplicative noises. Numerical examples for the semilinear stochastic space fractional partial differential equations are given.

The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.