A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems
The purpose of this paper is to propose a new collocation method for solving linear and nonlinear differential equations of high order as well as solving the differential equation on a very large interval. The new collocation method is based on a hybrid method combining the functions of the third ki...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-11-01
|
| Series: | Kuwait Journal of Science |
| Subjects: | |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/1052 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849727761123377152 |
|---|---|
| author | Saeid Jahangiri khosrow maleknejad Majid Tavassoli Kajani |
| author_facet | Saeid Jahangiri khosrow maleknejad Majid Tavassoli Kajani |
| author_sort | Saeid Jahangiri |
| collection | DOAJ |
| description | The purpose of this paper is to propose a new collocation method for solving linear and nonlinear differential equations of high order as well as solving the differential equation on a very large interval. The new collocation method is based on a hybrid method combining the functions of the third kind Chebyshev polynomials and Block-Pulse functions uses. In the proposed method, the large interval of the problems is divided to small sub-intervals and in each sub-interval, collocation method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution of the differential equation on each sub-intervals. The proposed method is more accurate than the previous methods. Numerical examples show the capability and effciency of the presented method compared to existing methods. |
| format | Article |
| id | doaj-art-979234bf6e4f432296bdaf486d9b9683 |
| institution | DOAJ |
| issn | 2307-4108 2307-4116 |
| language | English |
| publishDate | 2016-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-979234bf6e4f432296bdaf486d9b96832025-08-20T03:09:45ZengElsevierKuwait Journal of Science2307-41082307-41162016-11-01434381A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problemsSaeid Jahangiri0khosrow maleknejad1Majid Tavassoli KajaniDept. of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranIslamic Azad University Karaj BranchThe purpose of this paper is to propose a new collocation method for solving linear and nonlinear differential equations of high order as well as solving the differential equation on a very large interval. The new collocation method is based on a hybrid method combining the functions of the third kind Chebyshev polynomials and Block-Pulse functions uses. In the proposed method, the large interval of the problems is divided to small sub-intervals and in each sub-interval, collocation method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution of the differential equation on each sub-intervals. The proposed method is more accurate than the previous methods. Numerical examples show the capability and effciency of the presented method compared to existing methods.https://journalskuwait.org/kjs/index.php/KJS/article/view/1052Block-puls functionscollocation methodChebyshev polynomialshigher-order initial value problems (HOIVPs)hybrid collocation method. |
| spellingShingle | Saeid Jahangiri khosrow maleknejad Majid Tavassoli Kajani A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems Kuwait Journal of Science Block-puls functions collocation method Chebyshev polynomials higher-order initial value problems (HOIVPs) hybrid collocation method. |
| title | A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems |
| title_full | A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems |
| title_fullStr | A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems |
| title_full_unstemmed | A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems |
| title_short | A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems |
| title_sort | hybrid collocation method based on combining the third kind chebyshev polynomials and block pulse functions for solving higher order initial value problems |
| topic | Block-puls functions collocation method Chebyshev polynomials higher-order initial value problems (HOIVPs) hybrid collocation method. |
| url | https://journalskuwait.org/kjs/index.php/KJS/article/view/1052 |
| work_keys_str_mv | AT saeidjahangiri ahybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems AT khosrowmaleknejad ahybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems AT majidtavassolikajani ahybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems AT saeidjahangiri hybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems AT khosrowmaleknejad hybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems AT majidtavassolikajani hybridcollocationmethodbasedoncombiningthethirdkindchebyshevpolynomialsandblockpulsefunctionsforsolvinghigherorderinitialvalueproblems |