Numerical study of the singular nonlinear initial value problem with applications in astrophysics

• Published in: Results in physics Vol. 69; p. 108126
• Main Authors: El-Hady, Mahmoud Abd, Emadifar, Homan, El-Baghdady, Galal I., El-shenawy, Atallah
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2025; Elsevier
• Subjects: Astrophysics; Chelyshkov; Lane-Emden; Polytropic gas; Tau; Polytropic gas; Tau; Astrophysics; Chelyshkov; Lane-Emden
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2025.108126

The proposed models are very essential in several phenomena, especially astrophysics, cosmology, fluid mechanics, chemical engineering, and biophysics. The paper presents a exhaustive investigation of the convergence features and numerical performance of the Chelyshkov tau scheme when applied to the nonlinear singular Lane-Emden initial value problems. The Chelyshkov tau scheme is employed as the solution scheme to accurately and efficiently solve these models. The primary subject of the paper is to obtain an accurate, fast, and stable solution through the analysis of the convergence behavior and residual error associated with the proposed scheme. The manuscript presents comprehensive numerical results, highlighting the achieved accuracy and computational efficiency of the Chelyshkov tau scheme. The results are compared with analytical solutions or other established numerical methods, showcasing the superiority and effectiveness of the proposed scheme. •Applied the Chelyshkov tau scheme to solve nonlinear Lane-Emden problems effectively.•Investigated the convergence properties of the Chelyshkov tau scheme for stability.•Provided numerical results showcasing the scheme’s accuracy and efficiency.•Analyzed residual errors of the Chelyshkov tau scheme, confirming its performance.•Highlighted the models’ relevance in cosmology, fluid mechanics, and biophysics.