A Sixth-Order Cubic B-Spline Approach for Solving Linear Boundary Value Problems: An In-Depth Analysis and Comparative Study

Ram Kishun Lodhi, Moustafa S. Darweesh, Abdelkarim Aydi, Lioua Kolsi, Anil Sharma and Katta Ramesh ()
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Ram Kishun Lodhi: Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, Maharashtra, India
Moustafa S. Darweesh: Civil Engineering Department, College of Engineering, Northern Border University, Arar 73213, Saudi Arabia
Abdelkarim Aydi: French International School Victor Hugo, Gontardstraße 11, 60488 Frankfurt am Main, Germany
Lioua Kolsi: Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City 81451, Saudi Arabia
Anil Sharma: Department of Mathematics, University Institute of Sciences, Apex Institute of Technology—Computer Science and Engineering, Chandigarh University, Mohali 140413, Punjab, India
Katta Ramesh: Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya 47500, Selangor, Malaysia

Mathematics, 2024, vol. 12, issue 20, 1-16

Abstract: This research presents an efficient and highly accurate cubic B-spline method (CBSM) for solving second-order linear boundary value problems (BVPs). The method achieves sixth-order convergence, supported by rigorous error analysis, ensuring rapid error reduction with mesh refinement. The effectiveness of the CBSM is validated through four numerical examples, showcasing its accuracy, reliability, and computational efficiency, making it well-suited for large-scale problems. A comparative analysis with existing methods confirms the superior performance of the CBSM, positioning it as a practical and powerful tool for solving second-order BVPs.

Keywords: sixth-order convergence; cubic B-spline method; boundary value problems; error analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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