An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations
In order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like iterative methods to solve systems of nonlinear equations have combined to obtain the new algorithms. By this combination, two powerful hybrid met...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/9917774 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548025094897664 |
|---|---|
| author | Hooman Darvishi M. T. Darvishi |
| author_facet | Hooman Darvishi M. T. Darvishi |
| author_sort | Hooman Darvishi |
| collection | DOAJ |
| description | In order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like iterative methods to solve systems of nonlinear equations have combined to obtain the new algorithms. By this combination, two powerful hybrid methods are obtained. Necessary conditions for convergence of these methods are presented. Furthermore, the stability analysis of both algorithms is investigated. These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. Numerical results show promising convergence and stability for both new hybrid methods. |
| format | Article |
| id | doaj-art-ec7e08d965fe4a1c9c03bd4cdc31660b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ec7e08d965fe4a1c9c03bd4cdc31660b2025-02-03T06:42:40ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/9917774An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear EquationsHooman Darvishi0M. T. Darvishi1Department of MathematicsDepartment of MathematicsIn order to solve systems of nonlinear equations, two novel iterative methods are presented. The successive over-relaxation method and the Chebyshev-like iterative methods to solve systems of nonlinear equations have combined to obtain the new algorithms. By this combination, two powerful hybrid methods are obtained. Necessary conditions for convergence of these methods are presented. Furthermore, the stability analysis of both algorithms is investigated. These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. Numerical results show promising convergence and stability for both new hybrid methods.http://dx.doi.org/10.1155/2023/9917774 |
| spellingShingle | Hooman Darvishi M. T. Darvishi An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations Journal of Mathematics |
| title | An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations |
| title_full | An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations |
| title_fullStr | An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations |
| title_full_unstemmed | An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations |
| title_short | An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations |
| title_sort | analytical study on two high order hybrid methods to solve systems of nonlinear equations |
| url | http://dx.doi.org/10.1155/2023/9917774 |
| work_keys_str_mv | AT hoomandarvishi ananalyticalstudyontwohighorderhybridmethodstosolvesystemsofnonlinearequations AT mtdarvishi ananalyticalstudyontwohighorderhybridmethodstosolvesystemsofnonlinearequations AT hoomandarvishi analyticalstudyontwohighorderhybridmethodstosolvesystemsofnonlinearequations AT mtdarvishi analyticalstudyontwohighorderhybridmethodstosolvesystemsofnonlinearequations |