Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems

Ahmad, Abdulaziz Garba

doi:10.14445/22315373/ijmtt-v19p516

Cited by 12 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is proposed to solve the relationship g(x) = 0 by means of numerical methods: the bisection method, the Newton-Raphson method, the regula falsi method, combined methods, etc. [8][9][10]. To this end, the Department of Drilling and Geoengineering, at the Faculty of Drilling, Oil and Gas, AGH University of Science and Technology in Kraków, developed a numerical program, using the bisection method.…”

Section: Laminar Flow Of Reostable Fluids Through a Pipementioning

confidence: 99%

“…The solution of the g(x) = 0 relationship is proposed by means of the numerical methods: the bisection method, the Newton-Raphson method, the regula falsi method, combined methods, etc. [8,9,19]. The algorithm of solving Equation ( 23) by means of the secant method is presented in Figure 4.…”

Section: Determination Of Rheological Parameters and Resistances Of D...mentioning

confidence: 99%

See 1 more Smart Citation

Theory of the Vom Berg Rheological Model and Its Use in Cloud-Native Application

Wiśniowski

Orłowicz²

2022

Energies

View full text Add to dashboard Cite

Various technological fluids, such as drilling muds, drill-in fluids, fracturing fluids, spacers, washes and cement slurries are used in the wellbore drilling process. The fundamental issue, which needs to be addressed in order to become acquainted with the phenomena occurring during fluids flow through a circulatory system, is to establish mutual dependencies between a stream of fluid being pumped and flow resistances. The awareness of these dependencies enables the optimisation of hydraulic parameters in order to minimise costs and maximise drilling works safety. This article presents rheological models of drilling fluids and proposes the application of a new rheological model, not used in the drilling industry so far, namely the Vom Berg model. The model has been presented in other publications; however, there is an unsolved and unpublished problem of determining the effect of rheological parameters of the model on the value of resistance to laminar and turbulent flow. In this article, algorithms and Cloud-Native application enabling numerical determination of rheological properties of the Vom Berg fluid are presented. What is more, an algorithm for calculating pressure losses during the laminar flow of fluid in a pipe is provided. Taking an example from the industry, a practical application of the proposed calculation methodology is presented.

show abstract

Section: Laminar Flow Of Reostable Fluids Through a Pipementioning

confidence: 99%

Section: Determination Of Rheological Parameters and Resistances Of D...mentioning

confidence: 99%

Theory of the Vom Berg Rheological Model and Its Use in Cloud-Native Application

Wiśniowski

Orłowicz²

2022

Energies

View full text Add to dashboard Cite

show abstract

“…. Untuk fungsi f(x)=cos xexp(x) pada daerah interval [0,], metode bisection paling efektif dalam menentukan akar daripada metode lainnya [7].…”

Section: Pendahuluanunclassified

Nilai Awal Pada Metode Secant Yang Dimodifikasi Dalam Penentuan Akar Ganda Persamaan Non Linear

Batarius

SinLae

2019

jurnalmatrik

View full text Add to dashboard Cite

Determining the root of an equation means making the equation equal zero, (f (f) = 0). In engineering, there are often complex mathematical equations. With the numerical method approach, the equation can be searching for the value of the equation root. However, to find a double root approach with several numerical methods such as the bisection method, regulatory method, Newton-Raphson method, and Secant method, it is not efficient in determining multiple roots. This study aims to determine the roots of non-linear equations that have multiple roots using the modified Secant method. Besides knowing the effect of determining the initial value for the Secant method that is modifying in determining the non-linear root of persistence that has multiple roots. Comparisons were also make to other numerical methods in determining twin roots with the modified Secant method. A comparison is done to determine the initial value used. Simulations are performing on equations that have one single root and two or more double roots.

show abstract

“…Relevant situations in Physics where such problems are needed to be solved include finding the equilibrium position of an object, potential surface of a field and quantized energy level of confined structure [2]. As a matter of fact, the determination of any unknown appearing implicitly in scientific or engineering formulas, gives rise to root finding problem [3].…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

Azure¹,

Aloliga²,

Doabil³

2019

View full text Add to dashboard Cite

This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root-finding problem manually with the help of an TI-inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.

show abstract

Comparative Study of Bisection and Newton-Rhapson Methods of Root-Finding Problems

Cited by 12 publications

References 0 publications

Theory of the Vom Berg Rheological Model and Its Use in Cloud-Native Application

Theory of the Vom Berg Rheological Model and Its Use in Cloud-Native Application

Nilai Awal Pada Metode Secant Yang Dimodifikasi Dalam Penentuan Akar Ganda Persamaan Non Linear

Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

Contact Info

Product

Resources

About