Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations
dc.contributor.author | Pal, Kamal | * |
dc.contributor.author | Liu, Fang | * |
dc.contributor.author | Yan, Yubin | * |
dc.contributor.author | Roberts, Graham | * |
dc.date.accessioned | 2015-11-17T09:33:56Z | |
dc.date.available | 2015-11-17T09:33:56Z | |
dc.date.issued | 2015-06-17 | |
dc.identifier.citation | Pal, K., Liu, F., Yan, Y. & Roberts, G. (2015). Finite difference method for two-sided space-fractional partial differential equations. In I. Dimov, I. Farago & L. Vulkov (Eds.), Finite difference methods, theory and applications. 6th International Conference, FDM 2014 (pp. 307-314). Springer. | en |
dc.identifier.isbn | 9783319202396 | en |
dc.identifier.uri | http://hdl.handle.net/10034/582252 | |
dc.description.abstract | Finite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),10 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence. | |
dc.language.iso | en | en |
dc.publisher | Springer | en |
dc.relation.url | http://www.springer.com/gp/book/9783319202389 | en |
dc.subject | Finite difference method | en |
dc.subject | space-fractional partial differential equations | en |
dc.subject | error estimates | en |
dc.subject | stability | en |
dc.title | Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations | en |
dc.type | Book chapter | en |
dc.contributor.department | University of Chester | en |
html.description.abstract | Finite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),1<α<2 is obtained. A shifted implicit finite difference method is introduced for solving two-sided space-fractional partial differential equation and we prove that the order of convergence of the finite difference method is O(Δt+Δx^( min(3−α,β)) ),1<α<2,β>0 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence. | |
rioxxterms.publicationdate | 2015-06-17 |