Numerical solution of fractional partial differential equations using cubic B-spline wavelet collocation method
|
| Title | Numerical solution of fractional partial differential equations using cubic B-spline wavelet collocation method |
| Authors | |
| Abstract | Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic spline functions are presented. The main characteristic of the approach is that it converts such problems into those of solving a system of algebraic equations, which is suitable for numerical calculation. Numerical results demonstrate the validity and applicability of the method in solving fractional differential equation. The results from this method are good in terms of accuracy if the exact solution to fractional differential equation is in sufficient smooth. |
| Publisher | Advances in Computational Mathematics and its Applications |
| Date | 2012-06-10 |
| Source | 2167-6356 |
| Rights | Copyright NoticeProposed Creative Commons Copyright Notices1. Proposed Policy for Journals That Offer Open AccessAuthors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work´s authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal´s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).Proposed Policy for Journals That Offer Delayed Open AccessAuthors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication, with the work [SPECIFY PERIOD OF TIME] after publication simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work´s authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal´s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access). |