Evolutionary numerical approach for solving nonlinear singular periodic boundary value problems

Article type: Research Article

Authors: Ali, Mohamed R.^a | Hadhoud, Adel R.^b | Ma, Wen-Xiu^{c; d; e; f; *}

Affiliations: [a] Department of Basic Science, Faculty of Engineering at Benha, Benha University, Egypt | [b] Department of Mathematics, Faculty of Science, Menoufia University, Egypt | [c] Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China | [d] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia | [e] Department of Mathematics and Statistics, University of South Florida, Tampa, USA | [f] School of Mathematics, South China University of Technology, Guangzhou, China

Correspondence: [*] Corresponding author. Wen-Xiu Ma. E-mail: mawx@cas.usf.edu.

Abstract:  In this approximation study, a nonlinear singular periodic model in nuclear physics is solved by using the Hermite wavelets (HW) technique coupled with a numerical iteration technique such as the Newton Raphson (NR) one for solving the resulting nonlinear system. The stimulation of offering this numerical work comes from the aim of introducing a consistent framework that has as effective structures as Hermite wavelets. Two numerical examples of the singular periodic model in nuclear physics have been investigated to observe the robustness, proficiency, and stability of the designed scheme. The proposed outcomes of the HW technique are compared with available numerical solutions that established fitness of the designed procedure through performance evaluated on a multiple execution.

Keywords: Singular periodic systems in nuclear physics, Hermite wavelets, hybrid approach, Gaussian formula of integration, collocation technique

DOI: 10.3233/JIFS-201045

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 7723-7731, 2020