An integrated approach of the numerical simulation of nonlinear equations by modified bisection and regula falsi method

Inderjeet; Bhardwaj, Rashmi

doi:10.47974/JIM-2136

Open Access Research Article

An integrated approach of the numerical simulation of nonlinear equations by modified bisection and regula falsi method

Inderjeetyadavinderjeet386@gmail.comUniversity School of Basic and Applied Sciences (USBAS) Guru Gobind Singh Indraprastha University (GGSIPU)Dwarka, Delhi, 110078, IndiaView full profile → , ^*Rashmi BhardwajCorresponding authorrashmib@ipu.ac.inNonlinear Dynamics Research Lab University School of Basic and Applied Sciences (USBAS) Guru Gobind Singh Indraprastha University (GGSIPU)Nonlinear Dynamics Research Lab University School of Basic & Applied Sciences Guru Gobind Singh Indraprastha UniversityDwarka, Delhi, 110078, India0000-0002-0502-762XView full profile →

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pp. 1553–1571Vol. 28Issue 4June 2025DOI: 10.47974/JIM-2136XML

Received:: 10 Jul 2024
Published Online:: 06 Jun 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2136
Pages:: 1553–1571

Abstract

This paper presents an integrated approach to the numerical simulation of non-linear algebraic and transcendental equations using modified versions of the Bisection and Regula Falsi methods. The study aims to improve the efficiency and accuracy of root-finding algorithms for complex non-linear equations. We introduce modifications to the classical Bisection and Regula Falsi methods and compare their performance against traditional approaches. The research includes a comprehensive analysis of convergence rates, error margins, and computational complexity. Our findings demonstrate that the modified methods offer significant improvements in terms of speed and precision for a wide range of non-linear equations. The paper includes detailed tables presenting comparative results and discusses the implications of these findings for various fields of applied mathematics and engineering.

Keywords

Nonlinear equations Numerical simulation Root findings Bisection method Regula falsi method

Subject Classifications

65Hxx65H04

References

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