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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001512 |
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| Summary: | 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. |
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| ISSN: | 2666-8181 |