Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework
An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybr...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/9754906 |
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| author | H. R. Marzban S. Hajiabdolrahmani |
| author_facet | H. R. Marzban S. Hajiabdolrahmani |
| author_sort | H. R. Marzban |
| collection | DOAJ |
| description | An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybrid functions is introduced. The sparsity of this matrix significantly reduces the computation time and memory requirement. The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. Several numerical experiments are examined to verify the validity and applicability of the presented technique. |
| format | Article |
| id | doaj-art-90c6733f0af64eebacd22127c67d304a |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-90c6733f0af64eebacd22127c67d304a2025-02-03T06:11:08ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/97549069754906Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid FrameworkH. R. Marzban0S. Hajiabdolrahmani1Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranAn efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybrid functions is introduced. The sparsity of this matrix significantly reduces the computation time and memory requirement. The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. Several numerical experiments are examined to verify the validity and applicability of the presented technique.http://dx.doi.org/10.1155/2016/9754906 |
| spellingShingle | H. R. Marzban S. Hajiabdolrahmani Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework International Journal of Differential Equations |
| title | Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework |
| title_full | Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework |
| title_fullStr | Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework |
| title_full_unstemmed | Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework |
| title_short | Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework |
| title_sort | numerical solution of piecewise constant delay systems based on a hybrid framework |
| url | http://dx.doi.org/10.1155/2016/9754906 |
| work_keys_str_mv | AT hrmarzban numericalsolutionofpiecewiseconstantdelaysystemsbasedonahybridframework AT shajiabdolrahmani numericalsolutionofpiecewiseconstantdelaysystemsbasedonahybridframework |