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

Document Type : Research Article

Authors

• A.I. Kiri ¹
• M.Y. Waziri ²
• A.S. Halilu ³

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

² Numerical Optimization Group, Department of Mathematical Sciences, Bayero University, Kano, Nigeria.

³ Numerical Optimization Group, Bayero University, Kano, Nigeria, Department of Mathematics, Sule Lamido University, Kafin Hausa, Nigeria.

10.22067/ijnao.2022.74201.1083

Abstract

This study aims to present an accelerated derivative-free method for solving systems of nonlinear equations using a double direction approach. The approach approximates the Jacobian using a suitably formed diag-onal matrix by applying the acceleration parameter. Moreover, a norm descent line search is employed in the scheme to compute the optimal step length. Under the primary conditions, the proposed method’s global con-vergence 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 outperforms the existing Newton and inexact double step length methods.

Keywords

• Credit default swap (CDS)
• Acceleration parameter
• Matrix-free, Inexact line search
• Jacobian matrix

20.1001.1.24236977.2022.12.2.9.5

Main Subjects

• Optimization

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