Numerical solutions of higher order boundary value problems via wavelet approach

Advances in Difference Equations

Parin Chaipanya¹  Asad Ullah²  Sirajul Haq³  Shams Ul Arifeen³  Poom Kumam⁴  Abdul Ghafoor⁵ 

[1] Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uhit Rd, Bang Mod, Thung Khru, 10140, Bagnkok, Thailand;NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uhit Rd, Bang Mod, Thung Khru, 10140, Bagnkok, Thailand;Department of Mathematical Sciences, University of Lakki Marwat, 28420, Lakki Marwat, KP, Pakistan;Faculty of Engineering Sciences, GIK Institute, 23640, Topi, KP, Pakistan;Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uhit Rd, Bang Mod, Thung Khru, 10140, Bagnkok, Thailand;Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uhit Rd, Bang Mod, Thung Khru, 10140, Bagnkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Thailand;Institute of Numerical Sciences, Kohat University of Science and Technology, 26000, Kohat, KP, Pakistan;

关键词: Haar wavelet;    Higher order boundary value problem;    Quasilinearization;   

DOI  :  10.1186/s13662-021-03495-6

来源: Springer

【 摘 要 】

This paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with nonlinearity. Then, through collocation approach computing solutions of boundary value problems reduces to solve a system of linear equations which are computationally easy. The performance of the proposed technique is portrayed on some linear and nonlinear test problems including tenth, twelfth, and thirteen orders. Further convergence of the proposed method is investigated via asymptotic expansion. Moreover, computed results have been matched with the existing results, which shows that our results are comparably better. It is observed from convergence theoretically and verified computationally that by increasing the resolution level the accuracy also increases.

【 授权许可】

CC BY