Modification of the double direction approach for solving system of nonlinear equations with application to Chandrasekhar’s Integral equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 09 اسفند 1400  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.74201.1083

نویسندگان

Aliyu Ibrahim Kiri¹؛ Mohammed Yusuf Waziri ¹؛ Abubakar Sani Halilu ²

¹Department of Mathematical Sciences, Bayero University, Kano, Nigeria

²Department of Mathematics, Sule Lamido University, Kafin Hausa, Nigeria

چکیده

This study aims to present an accelerated derivative-free method for solving systems of nonlinear equations using a double direction approach. The approach approximated the Jacobian using a suitably formed diagonal matrix using the acceleration parameter. Moreover, norm descent line search is employed in the scheme to compute the optimal step length. Under the primary conditions, the proposed method's global convergence is proved. Numerical results are recorded in this paper using a set of large-scale test problems. Moreover, the new method is successfully used to address the problem of Chandrasekhar's integral equation problem appearing in radiative heat transfer. This method outperformed the existing Newton and inexact double step length (IDSL) methods.

کلیدواژه‌ها

Acceleration parameter؛ Matrix-free؛ Inexact line search؛ the Jacobian matrix