Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System
This research investigates differential-algebraic equations with higher index (index four). Specifically, a functional analytic approach is proposed to find the solution of (index four) Hessenberg differential-algebraic equations (DAEs). The approximate solution of the proposed functional approach f...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9621026 |
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| _version_ | 1832567768519540736 |
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| author | Ghazwa F. Abd |
| author_facet | Ghazwa F. Abd |
| author_sort | Ghazwa F. Abd |
| collection | DOAJ |
| description | This research investigates differential-algebraic equations with higher index (index four). Specifically, a functional analytic approach is proposed to find the solution of (index four) Hessenberg differential-algebraic equations (DAEs). The approximate solution of the proposed functional approach for a suitable separable Hilbert space is obtained with the help of the direct optimisation technique and Ritz basis functions method. Illustrations have been ranked from an 8 × 8 test system of index-four Hessenberg linear DAEs to a 4 × 4 DAE of rotating masses as well as an 8 × 8 differential-algebraic generator model, where it reformulated index-four linear Hessenberg DAEs. Their approximate solutions were obtained using the present approach with comparisons. The numerical results demonstrate the simplicity of the proposed approach and express suitable accuracy and efficiency. |
| format | Article |
| id | doaj-art-f8800995a268481da4f83e8bc160c6c2 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f8800995a268481da4f83e8bc160c6c22025-02-03T01:00:46ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9621026Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control SystemGhazwa F. Abd0Department of MathematicsThis research investigates differential-algebraic equations with higher index (index four). Specifically, a functional analytic approach is proposed to find the solution of (index four) Hessenberg differential-algebraic equations (DAEs). The approximate solution of the proposed functional approach for a suitable separable Hilbert space is obtained with the help of the direct optimisation technique and Ritz basis functions method. Illustrations have been ranked from an 8 × 8 test system of index-four Hessenberg linear DAEs to a 4 × 4 DAE of rotating masses as well as an 8 × 8 differential-algebraic generator model, where it reformulated index-four linear Hessenberg DAEs. Their approximate solutions were obtained using the present approach with comparisons. The numerical results demonstrate the simplicity of the proposed approach and express suitable accuracy and efficiency.http://dx.doi.org/10.1155/2022/9621026 |
| spellingShingle | Ghazwa F. Abd Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System Journal of Mathematics |
| title | Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System |
| title_full | Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System |
| title_fullStr | Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System |
| title_full_unstemmed | Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System |
| title_short | Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System |
| title_sort | functional approach for solving reduced order of index four hessenberg differential algebraic control system |
| url | http://dx.doi.org/10.1155/2022/9621026 |
| work_keys_str_mv | AT ghazwafabd functionalapproachforsolvingreducedorderofindexfourhessenbergdifferentialalgebraiccontrolsystem |