scholarly journals Quadratic Convergence Iterative Algorithms of Taylor Series for Solving Non-linear Equations

2020 ◽  
Vol 18 (02) ◽  
pp. 150-156
Author(s):  
Umair Khalid Qureshi ◽  
Zubair Ahmed Kalhoro ◽  
Rajab Ali Malookani ◽  
Sanaullah Dehraj ◽  
Shahid Hussain Siyal ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Quadratic Convergence ◽  
Linear Equations ◽  
Classical Problem ◽  
Iterative Algorithms ◽  
Initial Guess ◽  
Single Root ◽  
Newton Raphson ◽  
Steffensen Method ◽  
Raphson Method

Solving the root of algebraic and transcendental nonlinear equation f' (x) = 0 is a classical problem which has many interesting applications in computational mathematics and various branches of science and engineering. This paper examines the quadratic convergence iterative algorithms for solving a single root nonlinear equation which depends on the Taylor’s series and backward difference method. It is shown that the proposed iterative algorithms converge quadratically. In order to justify the results and graphs of quadratic convergence iterative algorithms, C++/MATLAB and EXCELL are used. The efficiency of the proposed iterative algorithms in comparison with Newton Raphson method and Steffensen method is illustrated via examples. Newton Raphson method fails if f' (x) = 0, whereas Steffensen method fails if the initial guess is not close enough to the actual solution. Furthermore, there are several other numerical methods which contain drawbacks and possess large number of evolution; however, the developed iterated algorithms are good in these conditions. It is found out that the quadratic convergence iterative algorithms are good achievement in the field of research for computing a single root of nonlinear equations.

scholarly journals MODIFIED QUADRATURE ITERATED METHODS OF BOOLE RULE AND WEDDLE RULE FOR SOLVING NON-LINEAR EQUATIONS

2021 ◽  
Vol 16 (2) ◽  
Author(s):  
Umair Khalid Qureshi
Keyword(s):  
Applied Sciences ◽  
Linear Equations ◽  
Numerical Results ◽  
Graphical Representations ◽  
Quadrature Method ◽  
Non Linear ◽  
Newton Raphson ◽  
Steffensen Method ◽  
Raphson Method ◽  
Non Linear Equations

This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.

scholarly journals NUMERICAL ITERATIVE METHOD OF OPEN METHODS WITH CONVERGE CUBICALLY FOR ESTIMATING NONLINEAR APPLICATION EQUATIONS

2021 ◽  
Author(s):  
Umair Khalid Qureshi
Keyword(s):  
Iterative Method ◽  
Newton Method ◽  
Numerical Technique ◽  
Classical Problem ◽  
Practical Application ◽  
Single Root ◽  
Modified Newton Method ◽  
Newton Raphson ◽  
Engineering Physics ◽  
Raphson Method

Finding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.

Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.

scholarly journals NILAI AWAL PADA METODE SECANT YANG DIMODIFIKASI DALAM PENENTUAN AKAR GANDA PERSAMAAN NON LINEAR

2019 ◽  
Vol 21 (1) ◽  
pp. 21-31
Author(s):  
Patrisius Batarius ◽  
Alfri Aristo SinLae
Keyword(s):  
Numerical Methods ◽  
Linear Equations ◽  
Secant Method ◽  
Multiple Roots ◽  
Initial Value ◽  
Single Root ◽  
Non Linear ◽  
Mathematical Equations ◽  
Raphson Method ◽  
Non Linear Equations

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.

Modelling of Thermodynamic Pressure – Composition – Temperature Relationships in the Systems of Metallic Hydride Forming Materials with Gaseous Hydrogen Using C++ Software

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Mapula Lucey Moropeng ◽  
Andrei Kolesnikov ◽  
Mykhaylo Lototskyy ◽  
Avhafunani Mavhungu
Keyword(s):  
Nonlinear Equation ◽  
Hydrogen Storage ◽  
Numerical Method ◽  
Metal Hydride ◽  
Metal Hydrides ◽  
Gaseous Hydrogen ◽  
Newton Raphson ◽  
Thermodynamic Pressure ◽  
The Relationship ◽  
Raphson Method

Abstract In this paper, the solution of the Lacher model describing the relationship between the Pressure – Composition, and Temperature (PCT diagrams) of AB5 type metal-hydrides (LaNi4.8Sn0.2, LmNi4.91Sn0.15, LaNi4.5Al0.5) for hydrogen storage using C ++ platform, with the help of a numerical method of nonlinear equation, Newton-Raphson method is presented. This study focuses on the development of a C ++ code to describe the iteration of Newton-Raphson for application in Hydrogen to Metal-Hydride systems.

scholarly journals Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative

2020 ◽  
Vol 3 (2) ◽  
pp. 155-160
Author(s):  
Vera Mandailina ◽  
Syaharuddin Syaharuddin ◽  
Dewi Pramita ◽  
Malik Ibrahim ◽  
Habib Ratu Perwira Negara
Keyword(s):  
Taylor Series ◽  
Linear Equations ◽  
Computational Design ◽  
Qualitative Comparison ◽  
Comparison Results ◽  
Starting Point ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Some of the numeric methods for solutions of non-linear equations are taken from a derivative of the Taylor series, one of which is the Newton-Raphson method. However, this is not the only method for solving cases of non-linear equations. The purpose of the study is to compare the accuracy of several derivative methods of the Taylor series of both single order and two-order derivatives, namely Newton-Raphson method, Halley method, Olver method, Euler method, Chebyshev method, and Newton Midpoint Halley method. This research includes qualitative comparison types, where the simulation results of each method are described based on the comparison results. These six methods are simulated with the Wilkinson equation which is a 20-degree polynomial. The accuracy parameters used are the number of iterations, the roots of the equation, the function value f (x), and the error. Results showed that the Newton Midpoint Halley method was the most accurate method. This result is derived from the test starting point value of 0.5 to the equation root x = 1, completed in 3 iterations with a maximum error of 0.0001. The computational design and simulation of this iterative method which is a derivative of the two-order Taylor series is rarely found in college studies as it still rests on the Newton-Raphson method, so the results of this study can be recommended in future learning.

EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB

2017 ◽  
Vol 1 (1) ◽  
pp. 95
Author(s):  
Siti Nurhabibah Hutagalung
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Abstract - The study of the characteristics of non-liier functions can be carried out experimentally and theoretically. One part of theoretical analysis is computation. For computational purposes, numerical methods can be used to solve equations complicated, for example non-linear equations. There are a number of numerical methods that can be used to solve nonlinear equations, the Newton-Raphson method. Keywords - Numerical, Newton Raphson.

THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 87-99 ◽  
Author(s):  
HANS RUDOLF SCHNEEBELI ◽  
THOMAS P. WIHLER
Keyword(s):  
Quadratic Convergence ◽  
Chaotic Behavior ◽  
Size Control ◽  
Original Method ◽  
Control Procedure ◽  
Step Size ◽  
Newton Raphson ◽  
Low Dimensional ◽  
Adaptive Step ◽  
Raphson Method

The Newton–Raphson method for solving nonlinear equations f(x) = 0 in ℝn is discussed within the context of ordinary differential equations. This framework makes it possible to reformulate the scheme by means of an adaptive step size control procedure that aims at reducing the chaotic behavior of the original method without losing the quadratic convergence close to the roots. The performance of the modified scheme is illustrated with a few low-dimensional examples.

scholarly journals A Computer Model for the Hydraulic Analysis of Open Channel Cross Sections

1996 ◽  
Vol 1 ◽  
pp. 57
Author(s):  
W. H. Shayya ◽  
R. H. Mohtar ◽  
M. S Baasiri
Keyword(s):  
Computer Model ◽  
Cross Sections ◽  
Solution Process ◽  
Initial Guess ◽  
Hydraulic Design ◽  
Implicit Equations ◽  
Actual Solution ◽  
Newton Raphson ◽  
Geometric Elements ◽  
Raphson Method

Irrigation and hydraulic engineers are often faced with the difficulty of tedious trial solutions of the Manning equation to determine the various geometric elements of open channels. This paper addresses the development of a computer model for the design of the most commonly used channel-sections. The developed model is intended as an educational tool. It may be applied to the hydraulic design of trapezoidal , rectangular, triangular, parabolic, round-concered rectangular, and circular cross sections. Two procedures were utilized for the solution of the encountered implicit equations; the Newton-Raphson and the Regula-Falsi methods.  In order to initiate the solution process , these methods require one and two initial guesses, respectively. Tge result revealed that the Regula-Flasi method required more iterations to coverage to the solution compared to the Newton-Raphson method, irrespective of the nearness of the initial guess to the actual solution. The average number of iterations for the Regula-Falsi method was approximately three times that of the Newton-Raphson method.

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