The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations
Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based me...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/638026 |
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| author | W. K. Zahra S. M. Elkholy |
| author_facet | W. K. Zahra S. M. Elkholy |
| author_sort | W. K. Zahra |
| collection | DOAJ |
| description | Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented. |
| format | Article |
| id | doaj-art-f33118f678f94d22badb62e3fb02e5e1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f33118f678f94d22badb62e3fb02e5e12025-02-03T01:09:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/638026638026The Use of Cubic Splines in the Numerical Solution of Fractional Differential EquationsW. K. Zahra0S. M. Elkholy1Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, 31521 Tanta, EgyptDepartment of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh University, Kafr El Sheikh, EgyptFractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented.http://dx.doi.org/10.1155/2012/638026 |
| spellingShingle | W. K. Zahra S. M. Elkholy The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations International Journal of Mathematics and Mathematical Sciences |
| title | The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations |
| title_full | The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations |
| title_fullStr | The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations |
| title_full_unstemmed | The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations |
| title_short | The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations |
| title_sort | use of cubic splines in the numerical solution of fractional differential equations |
| url | http://dx.doi.org/10.1155/2012/638026 |
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