A new method for solving nonlinear equations by Taylor expansion (original) (raw)
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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.