A new method for solving nonlinear equations by Taylor expansion (original) (raw)
The aim of this paper is to construct an efficient iterative method to solve non linear equations. One new iterative method for solving algebraic and transcendental equations is presented using a Taylor series formula . using the , the Newton’s method and the an Improve iterative method and the result compared. It was observed that the Newton method required more number of iteration in comparison to improve iterative method. By the use of numerical experiments to show that this method are more efficient than Newton – Raphson method.
Numerical Study of Some Iterative Methods for Solving Nonlinear Equations
IJEST, 2016
In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations is presented by the different formulae. Using bisection method , secant method and the Newton's iterative method and their results are compared. The software, matlab 2009a was used to find the root of the function for the interval [0,1]. Numerical rate of convergence of root has been found in each calculation. It was observed that the Bisection method converges at the 47 iteration while Newton and Secant methods converge to the exact root of 0.36042170296032 with error level at the 4th and 5th iteration respectively. It was also observed that the Newton method required less number of iteration in comparison to that of secant method. However, when we compare performance, we must compare both cost and speed of convergence [6]. It was then concluded that of the three methods considered, Secant method is the most effective scheme. By the use of numerical experiments to show that secant method are more efficient than others.
New Third-order Iterative Method for Solving Nonlinear Equations.
In this paper, we present a new third-order iterative method for solving nonlinear equations. The new method is based on Newton-Raphson method and Taylor series method. The efficiency of the method is tested on several numerical examples. It is observed that the method is comparable with the well-known existing methods and in many cases gives better results.
Modified Iterative Method for Solving Nonlinear Equation
In this paper, we present new one- and two-steps iterative methods for solving nonlinear equation f(x)=0. It is proved here that the iterative methods converge of order three and six respectively. Several numerical examples are given to illustrate the performance and to show that the iterative methods in this paper give better result than the compared methods
A New Computational Approach for Nonlinear Equations
2008
The aim of this paper is to construct a new iterative method to solve nonlinear equations. The new method is based on Newton-Raphson method and power series. The convergence of this new scheme is addressed and a cubic order of convergence, at least, is established. To illustrate the method some examples, mainly from references have been presented, so one would be able to compare the results of the same problems obtained by applying different methods, and the advantage of the new method can be recognized.
A new iterative method for solving nonlinear equations
Applied Mathematics and Computation, 2006
In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.
Quadratic Convergence Iterative Algorithms of Taylor Series for Solving Non- linear Equations
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.
A new hybrid iteration method for solving algebraic equations
Applied Mathematics and Computation, 2008
A new hybrid iteration method (the hybrid's name was used by Luo [Xing-Guo Luo, Applied Mathematics and Computation 171 (2) (2005) 1171-1183]) has been proposed for solving a non linear algebraic equation f(x) = 0, by using Taylor's theorem. In this paper, we proposed a new hybrid iteration method and we show by one equation that this new hybrid iteration method is more quickly convergent than Newton's method and hence than hybrid iteration method.
A New Third-Order Iteration Method for Solving Nonlinear Equations
Open Journal of Mathematical Analysis
In this paper, we establish a two step third-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.442 which is greater than Newton-Raphson method. It is important to note that our method is performing very well in comparison to fixed point method and the method discussed by Kang et al. (Abstract and applied analysis; volume 2013, Article ID 487060).
Comparison of Some Iterative Methods of Solving Nonlinear Equations
International Journal of Theoretical and Applied Mathematics, 2018
This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton's method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.
AN ITERATIVE METHOD FOR SOLVING NON-LINEAR TRANSCENDENTAL EQUATIONS
J. Math. Comput. Sci., 2020
In this paper, we introduced a new method to compute a non-zero real root of the transcendental equations. The proposed method results in better approximate root than the existing methods such as bisection method, regula-falsi method and secant method. The implementation of the proposed method in MATLAB is applied on different problems to demonstrate the applicability of the method. The proposed method is better in reducing error rapidly, hence converges faster as compared to the existing methods. This method will help to employ in the commercial package for finding a non-zero real root of a given nonlinear equations (transcendental, algebraic and exponential).
NUMERICAL HYBRID ITERATIVE TECHNIQUE FOR SOLVING NONLINEAR EQUATIONS IN ONE VARIABLE
JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES, 2021
In recent years, some improvements have been suggested in the literature that has been a better performance or nearly equal to existing numerical iterative techniques (NIT). The efforts of this study are to constitute a Numerical Hybrid Iterative Technique (NHIT) for estimating the real root of nonlinear equations in one variable (NLEOV) that accelerates convergence. The goal of the development of the NHIT for the solution of an NLEOV assumed various efforts to combine the different methods. The proposed NHIT is developed by combining the Taylor Series method (TSM) and Newton Raphson's iterative method (NRIM). MATLAB and Excel software has been used for the computational purpose. The developed algorithm has been tested on variant NLEOV problems and found the convergence is better than bracketing iterative method (BIM), which does not observe any pitfall and is almost equivalent to NRIM.
An iterative method of order four based on power series for solving a nonlinear equation
2014
In this paper, a one-point iteration formula for solving a nonlinear equation is presented. The formula is derived by finding a coefficient of a power series for updating Newton method. We show analytically that the method is of order four for a simple root. We verify the theoretical result on relevant numerical problems and compare the behavior of the propose method with some existing methods.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINEAR EQUATION
Applied Mathematics and Sciences: An International Journal (MathSJ), 2019
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
Three New Iterative Methods for Solving Nonlinear Equations
In this paper, we present a family of new iterative methods for solving nonlinear equations based on Newton's method. The order of convergence and corresponding error equations of the obtained iteration formulae are derived analytically and with the help of Maple. Some numerical examples are given to illustrate the efficiency of the presented methods, so one would be able to compare the results of the same problems obtained by applying different methods, and the advantage of the new methods can be recognized.
New three step derivative free iterative method for solving nonlinear equations
Malaya Journal of Matematik
In this paper, we present a three step derivative free iterative method for solving nonlinear equations f (x) = 0. We discuss the convergence criteria of this new derivative free iterative method. A comparison with other existing methods is also given. The aim of this paper is to develop a new derivative free iterative method to find the approximation of the root α is nonlinear equations f (x) = 0, without the evaluation of the derivatives. This new method is based on Steffensen's method [11]. It is prove that the new method has cubic convergence. The benefit of this method is that it does not need to calculate any derivative. Numerical comparisons are made with other existing methods to show the better performance of the presented method.
A new iterative method to compute nonlinear equations
Applied Mathematics and Computation, 2006
The aim of this paper is to construct a new efficient iterative method to solve nonlinear equations. The new method is based on the proposals of Abbasbandy on improving the order of accuracy of Newton-Raphson method [S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation 145 887-893] and on the proposals of Babolian and Biazar on improving the order of accuracy of AdomianÕs decomposition method [E. Babolian, J. Biazar, On the order of convergence of Adomian method, Applied Mathematics and Computation 130 (2002) 383-387]. The convergence of the new scheme is proved and at least the cubic order of convergence is established. Several examples are presented and compared to other methods, showing the accuracy and fast convergence of this new method. Also, it is shown in this paper, that the modified AdomianÕs method developed by Babolian and Biazar to solve nonlinear equations [E. Babolian, J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation 132 (2002) 167-172] should be slightly modified, due to the fact that convergence of AdomianÕs method does not ensure convergence of the modified method. An example illustrates 0096-3003/$ -see front matter Ó (M. Basto). Applied Mathematics and Computation 173 (2006) 468-483
Improved Newton’s Method for Solving Nonlinear Equations (1998)
An iterative scheme is introduced improving Newton's method which is widely used for solving nonlinear equations. The method is developed for both functions of one variable and two variables. Proposed scheme replaces the rectangular approximation of the indefinite integral involved in Newton's Method by a trapezium. It is shown that 'the order of convergence of the new method is at least three for functions of one variable. Computational results overwhelmingly support this theory and the computational order of convergence is even more than three for certain functions. Algorithms constructed were implemented by using the high level computer language Turbo Pascal (Ver. 7) Key words: Convergence, Newton's method, Improved Newton's method, Nonlinear equations, Root finding, Order of convergence, Iterative methods
JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES, 2021
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.
Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations
Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 2021
Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.