A modified scheme to the multiple shooting method for BVPs
A significant modification of the multiple shooting method for solving nth order boundary value problems (BVPs) is presented. Initially, the mathematical foundation of this modification is elucidated. The method discretizes the domain of the original problem into N subintervals to construct semi-ana...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-04-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016825000985 |
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| author | Samad Kheybari Mohammad Taghi Darvishi Farzaneh Alizadeh Salah Mahmoud Boulaaras Kamyar Hosseini |
| author_facet | Samad Kheybari Mohammad Taghi Darvishi Farzaneh Alizadeh Salah Mahmoud Boulaaras Kamyar Hosseini |
| author_sort | Samad Kheybari |
| collection | DOAJ |
| description | A significant modification of the multiple shooting method for solving nth order boundary value problems (BVPs) is presented. Initially, the mathematical foundation of this modification is elucidated. The method discretizes the domain of the original problem into N subintervals to construct semi-analytical approximate solutions that are continuously differentiable up to the (n−1)-th order. The accuracy of the solution is improved by minimizing the L2-norm of the residual functions within each subinterval. The resulting piecewise continuous solution is represented by polynomials or basis functions, ensuring smoothness and derivative continuity at the junctions. The effectiveness of the proposed method is demonstrated through various test problems, including a ninth-order linear problem, a tenth-order nonlinear problem, and several stiff problems, with results showing superior performance compared to the standard shooting method and the modified decomposition method. Additionally, the empirical convergence orders are computed, and the computation times required for each test problem are reported, further highlighting the efficiency and accuracy of the approach. |
| format | Article |
| id | doaj-art-68bf7dcfe7c543e3a056365fd8c29e17 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-68bf7dcfe7c543e3a056365fd8c29e172025-01-31T05:10:12ZengElsevierAlexandria Engineering Journal1110-01682025-04-01118649663A modified scheme to the multiple shooting method for BVPsSamad Kheybari0Mohammad Taghi Darvishi1Farzaneh Alizadeh2Salah Mahmoud Boulaaras3Kamyar Hosseini4Faculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, Turkey; Corresponding authors.Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, IranFaculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, Turkey; Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey; Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, TurkeyDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; Corresponding authors.Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey; Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, TurkeyA significant modification of the multiple shooting method for solving nth order boundary value problems (BVPs) is presented. Initially, the mathematical foundation of this modification is elucidated. The method discretizes the domain of the original problem into N subintervals to construct semi-analytical approximate solutions that are continuously differentiable up to the (n−1)-th order. The accuracy of the solution is improved by minimizing the L2-norm of the residual functions within each subinterval. The resulting piecewise continuous solution is represented by polynomials or basis functions, ensuring smoothness and derivative continuity at the junctions. The effectiveness of the proposed method is demonstrated through various test problems, including a ninth-order linear problem, a tenth-order nonlinear problem, and several stiff problems, with results showing superior performance compared to the standard shooting method and the modified decomposition method. Additionally, the empirical convergence orders are computed, and the computation times required for each test problem are reported, further highlighting the efficiency and accuracy of the approach.http://www.sciencedirect.com/science/article/pii/S1110016825000985Boundary value problemsStiff problemsNumerical methodsShooting methodMultiple shooting method |
| spellingShingle | Samad Kheybari Mohammad Taghi Darvishi Farzaneh Alizadeh Salah Mahmoud Boulaaras Kamyar Hosseini A modified scheme to the multiple shooting method for BVPs Alexandria Engineering Journal Boundary value problems Stiff problems Numerical methods Shooting method Multiple shooting method |
| title | A modified scheme to the multiple shooting method for BVPs |
| title_full | A modified scheme to the multiple shooting method for BVPs |
| title_fullStr | A modified scheme to the multiple shooting method for BVPs |
| title_full_unstemmed | A modified scheme to the multiple shooting method for BVPs |
| title_short | A modified scheme to the multiple shooting method for BVPs |
| title_sort | modified scheme to the multiple shooting method for bvps |
| topic | Boundary value problems Stiff problems Numerical methods Shooting method Multiple shooting method |
| url | http://www.sciencedirect.com/science/article/pii/S1110016825000985 |
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