scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

scholarly journals An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression

2020 ◽  
Vol 12 (6) ◽  
pp. 50
Author(s):  
Christian Vanhille
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Secant Method ◽  
Variable Order ◽  
Discretization Step ◽  
Newton Raphson ◽  
Analytic Expression ◽  
The One ◽  
Derivatives Of ◽  
Raphson Method

We propose an iterative method to evaluate the roots of nonlinear equations. This Secant-based technique approximates the derivatives of the function numerically through a constant discretization step h disassociated from the iterative progression. The algorithm is developed, implemented, and tested. Its order of convergence is found to be h-dependent. The results obtained corroborate the theoretical deductions and evidence its excellent behavior. For infinitesimal h-values, the algorithm accelerates the convergence of the Secant method to order 2 (the one of the Newton-Raphson method) with no need for analytic expression of derivatives (the advantage of the Secant method).

scholarly journals A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Sanaullah Jamali
Keyword(s):  
Numerical Analysis ◽  
Numerical Solution ◽  
Bisection Method ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Derivative Free Method ◽  
Newton Raphson ◽  
Transcendental Equations ◽  
Regula Falsi Method ◽  
Raphson Method

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it’s observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods.

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.

scholarly journals On the Modification of Newton-Secant Method in Solving Nonlinear Equations for Multiple Zeros of Trigonometric Function

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 84-96
Author(s):  
Juhari Juhari
Keyword(s):  
Mathematical Model ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Trigonometric Function ◽  
Secant Method ◽  
Second Step ◽  
Initial Values ◽  
Newton Raphson ◽  
Modified Formula ◽  
Raphson Method

This study discusses the analysis of the modification of Newton-Secant method and solving nonlinear equations having a multiplicity of  by using a modified Newton-Secant method. A nonlinear equation that has a multiplicity   is an equation that has more than one root. The first step is to analyze the modification of the Newton-Secant method, namely to construct a mathematical model of the Newton-Secant method using the concept of the Newton method and the concept of the Secant method. The second step is to construct a modified mathematical model of the Newton-Secant method by adding the parameter . After obtaining the modified formula for the Newton-Secant method, then applying the method to solve a nonlinear equations that have a multiplicity . In this case, it is applied to the nonlinear equation which has a multiplicity of . The solution is done by selecting two different initial values, namely  and . Furthermore, to determine the effectivity of this method, the researcher compared the result with the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified. The obtained results from the analysis of modification of Newton-Secant method is an iteration formula of the modified Newton-Secant method. And for the result of  using a modified Newton-Secant method with two different initial values, the root of  is obtained approximately, namely  with less than iterations. whereas when using the Newton-Raphson method, the Secant method, and the Newton-Secant method, the root  is also approximated, namely  with more than  iterations. Based on the problem to find the root of the nonlinear equation  it can be concluded that the modified Newton-Secant method is more effective than the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

scholarly journals Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 169
Author(s):  
Avram Sidi
Keyword(s):  
Nonlinear Equations ◽  
Local Convergence ◽  
Real Root ◽  
Numerical Procedure ◽  
Secant Method ◽  
Convergence Theory ◽  
Simple Complex ◽  
Real Roots ◽  
Complex Roots ◽  
Appl Math

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

scholarly journals PEMAHAMAN METODE NUMERIK MENGGUNAKAN PEMPROGRMAN MATLAB (Studi Kasus : Metode Secant)

2017 ◽  
Vol 1 (1) ◽  
pp. 89
Author(s):  
Melda Panjaitan
Keyword(s):  
Approximate Solution ◽  
Problem Solving ◽  
Numerical Methods ◽  
Numerical Method ◽  
Mathematical Problem ◽  
Secant Method ◽  
Mathematical Problem Solving ◽  
Real Solution ◽  
True Solution ◽  
Solution Approach

Abstract - The numerical method is a powerful mathematical problem solving tool. With numerical methods, we get a solution that approaches or approaches a true solution so that a numerical solution is also called an approximate solution or solution approach, but almost the solution can be made as accurately as we want. The solution almost certainly isn't exactly the same as the real solution, so there is a difference between the two. This difference is called an error. the solution using numerical methods is always in the form of numbers. The secant method requires two initial estimates that must enclose the roots of the equation. Keywords - Numerical Method, Secant Method

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 A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Nurnadiah Zamri ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Numerical Results ◽  
Parametric Form ◽  
Solution Point ◽  
New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coefficients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient. 

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