Employing CNPS and CPS approaches to calculate numerical roots of ninth-order linear and nonlinear boundary value problems

Aasma Khalid, Inamul Haq (), Akmal Rehan (), Hashim M. Alshehri () and M. S. Osman
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Aasma Khalid: Department of Mathematics, GCW University, Faisalabad 38023, Pakistan
Inamul Haq: Department of Mathematics, GCW University, Faisalabad 38023, Pakistan
Akmal Rehan: Department of Computer Science, University of Agriculture, Faisalabad 38023, Pakistan
Hashim M. Alshehri: Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah 21521, Saudi Arabia
M. S. Osman: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 10, 1-28

Abstract: The extremely accurate findings of ninth-order linear and nonlinear BVPs are described in this paper. CNPS and CPS are used to find out the numerical roots of linear and nonlinear, ninth-order BVPs. The proposed methods transform the ninth-order BVPs into a system of linear equations. The algorithms developed in this study not only provide approximate solutions to the BVPs using CNPS and CPS, but they also estimate the derivatives from the first to the ninth-order of the analytical solution simultaneously. These approaches are implemented across five diverse problems, showcasing the effectiveness of these techniques by utilizing step sizes of h=1/10 and h=1/5. In order to gauge the accuracy of the methods, a comparison is drawn between the outcomes and the exact solutions, which are then presented in tabular and graphical format. The precision of these techniques is demonstrated through a detailed investigation and is found to be superior to the CBS, the Petrov–Galerkin Method (PGM) using Splines functions as basis functions and Septic B Splines functions as weight functions, the collocation method for ninth-order BVPs by Quintic B Splines and Sextic B Splines as evidenced by the comparison of AEs of CPS and CNPS with these alternative methods.

Keywords: Boundary value problems; cubic spline; polynomial and nonpolynomial splines; absolute errors; central finite difference approximations (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124501213

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