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,
Katta Ramesh
Affiliations
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
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.
