Quadrature Rule Based Iterative Method for the Solution of Non-Linear Equations | [Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences • 2019]

Author(s):

1. Umair Khalid Qureshi: Department of Business Administration, Shaheed Benazir Bhutto University,Sanghar, Sindh,Pakistan

2. Irfan Ali Bozdar: Department of Information Technology, Shaheed Benazir Bhutto University,Shaheed Benaziraba, Sindh,Pakistan

3. Aliya Pirzada: Department of Business Administration, Shaheed Benazir Bhutto University,Naushahro Feroze, Sindh,Pakistan

4. Muzaffar Bashir Arain: Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science & Technology,Nawabshah, Sindh,Pakistan

Abstract:

This research has suggested a quadrature rule based iterative method for the solution of non-linear algebraic and transcendental equations. The proposed iterated method is derived from Quadrature Formula and Numerical Technique. The quadrature rule based iterative method is converged quadratically, and it is free from pitfall. Few of physical non-linear problems to demonstrate the competency of proposed iterative method with the assessment of Steffensen Method and Newton Raphson Method. C++ and EXCEL have been used to examine the numerical results and graphical illustration of quadrature rule based iterative method. Hence, from several examples illustrate that the convergence and efficiency of the quadrature rule based iterative method is better than Steffensen Method and Newton Raphson Method.

Page(s): 39-43

DOI: DOI not available

Published: Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 56, Issue: 1, Year: 2019

Keywords:

Error , Nonlinear problems , Convergence analysis , Quadrature formula , Second order method

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