Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems
It has long been a concern of researchers to address the challenges of solving higher-order differential equations. In order to approximate 11th-order boundary value problems (BVPs), this work presents a novel numerical approach that combines decomposition techniques with polynomial and Non-Polynomi...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001512 |
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| author | Aasma Khalid Inamul Haq Akmal Rehan M.S. Osman |
| author_facet | Aasma Khalid Inamul Haq Akmal Rehan M.S. Osman |
| author_sort | Aasma Khalid |
| collection | DOAJ |
| description | It has long been a concern of researchers to address the challenges of solving higher-order differential equations. In order to approximate 11th-order boundary value problems (BVPs), this work presents a novel numerical approach that combines decomposition techniques with polynomial and Non-Polynomial Splines of third order. The method starts with a decomposition process that breaks down 11th-order BVPs into a system of second-order BVPs, breaking the problem down into smaller, more manageable parts. First-order derivatives are approximated using finite central differences, and each second-order ordinary differential equation is solved using both spline methods. These methods improve accuracy and efficiency when handling complex BVPs by providing a thorough framework for solving high-order differential equations. Comparing numerical responses with the precise response on a variety of examples was part of the numerical evaluations. |
| format | Article |
| id | doaj-art-a7a6785be2f743de865ef96e33442628 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-a7a6785be2f743de865ef96e334426282025-08-20T02:17:09ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410122410.1016/j.padiff.2025.101224Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systemsAasma Khalid0Inamul Haq1Akmal Rehan2M.S. Osman3Department of Mathematics, GC Women University Faisalabad, 38023, Pakistan; Corresponding authors.Department of Mathematics, GC Women University Faisalabad, 38023, PakistanDepartment of Computer Science, University of Agriculture Faisalabad, 38023, PakistanMathematics Department, Faculty of Sciences, Umm AI-Qura University, Makkah 21955, Saudi Arabia; Corresponding authors.It has long been a concern of researchers to address the challenges of solving higher-order differential equations. In order to approximate 11th-order boundary value problems (BVPs), this work presents a novel numerical approach that combines decomposition techniques with polynomial and Non-Polynomial Splines of third order. The method starts with a decomposition process that breaks down 11th-order BVPs into a system of second-order BVPs, breaking the problem down into smaller, more manageable parts. First-order derivatives are approximated using finite central differences, and each second-order ordinary differential equation is solved using both spline methods. These methods improve accuracy and efficiency when handling complex BVPs by providing a thorough framework for solving high-order differential equations. Comparing numerical responses with the precise response on a variety of examples was part of the numerical evaluations.http://www.sciencedirect.com/science/article/pii/S2666818125001512CubicSplinesPolynomialAbsolute errorsCentral finite difference approximationsNon-polynomial |
| spellingShingle | Aasma Khalid Inamul Haq Akmal Rehan M.S. Osman Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems Partial Differential Equations in Applied Mathematics Cubic Splines Polynomial Absolute errors Central finite difference approximations Non-polynomial |
| title | Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| title_full | Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| title_fullStr | Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| title_full_unstemmed | Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| title_short | Developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| title_sort | developing and applying cubic spline method for the solution of boundary value problems in complex physical and engineering systems |
| topic | Cubic Splines Polynomial Absolute errors Central finite difference approximations Non-polynomial |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001512 |
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