General 2 × 2 system of nonlinear integral equations and its approximate solution
In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization...
| Main Authors: | , , , |
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| Format: | Article |
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2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/79977/ |
| _version_ | 1848858800466952192 |
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| author | Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. |
| author_facet | Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. |
| author_sort | Eshkuvatov, Z. K. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization method. Nystrom method with Gauss–Legendre quadrature is applied for the kernel integrals and Newton forwarded interpolation formula is used for finding values of unknown functions at the selected node points. Existence and uniqueness solution of the problems are proved and accuracy of the quadrature formula together with convergence of the proposed method are obtained. Finally, numerical examples are provided to show the validity and efficiency of the method presented. Numerical results reveal that the proposed methods is efficient and accurate. Comparisons with other methods for the same problem are also presented. |
| first_indexed | 2025-11-15T12:19:12Z |
| format | Article |
| id | upm-79977 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T12:19:12Z |
| publishDate | 2019 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-799772023-04-14T02:02:19Z http://psasir.upm.edu.my/id/eprint/79977/ General 2 × 2 system of nonlinear integral equations and its approximate solution Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. In this note, we consider a general 2 × 2 system of nonlinear Volterra type integral equations. The modified Newton method (modified NM) is used to reduce the nonlinear problems into 2 × 2 linear system of algebraic integral equations of Volterra type. The latter equation is solved by discretization method. Nystrom method with Gauss–Legendre quadrature is applied for the kernel integrals and Newton forwarded interpolation formula is used for finding values of unknown functions at the selected node points. Existence and uniqueness solution of the problems are proved and accuracy of the quadrature formula together with convergence of the proposed method are obtained. Finally, numerical examples are provided to show the validity and efficiency of the method presented. Numerical results reveal that the proposed methods is efficient and accurate. Comparisons with other methods for the same problem are also presented. 2019 Article PeerReviewed Eshkuvatov, Z. K. and Hameed, Hameed Husam and Taib, B. M. and Nik Long, N. M. A. (2019) General 2 × 2 system of nonlinear integral equations and its approximate solution. pp. 528-546. https://www.sciencedirect.com/science/article/pii/S0377042719302201 10.1016/j.cam.2019.04.025 |
| spellingShingle | Eshkuvatov, Z. K. Hameed, Hameed Husam Taib, B. M. Nik Long, N. M. A. General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title | General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title_full | General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title_fullStr | General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title_full_unstemmed | General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title_short | General 2 × 2 system of nonlinear integral equations and its approximate solution |
| title_sort | general 2 × 2 system of nonlinear integral equations and its approximate solution |
| url | http://psasir.upm.edu.my/id/eprint/79977/ http://psasir.upm.edu.my/id/eprint/79977/ http://psasir.upm.edu.my/id/eprint/79977/ |