Juhari, Juhari (2021) On the modification of newtonsecant method in solving nonlinear equations for multiple zeros of trigonometric function. Cauchy: Jurnal Matematika Murni dan Aplikasi, 7 (1). pp. 8496. ISSN 20860382

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Abstract
This study discusses the construction of mathematical model modification of NewtonSecant method and solving nonlinear equations for multiple zeros by using a modified NewtonSecant method. A nonlinear equations for multiple zeros or multiplicity m>1 is an equation that has more than one root. The first step is to construct of mathematical model NewtonSecant method and its modification, namely to construct a mathematical model of the NewtonSecant 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 NewtonSecant method by adding the parameter θ. After obtaining the formula for the modification NewtonSecant method, then applying the method to solve a nonlinear equations for multiple zeros. In this case, it is applied to the nonlinear equation trigonometric function f(x)=(co s^2x+x)^5 which has a multiplicity of m = 5. The solution is done by selecting four different initial guess, namely 2;0,8;0,2 and 2. Furthermore, to determine the effectivity of this method, the researcher compared the result with the NewtonRaphson method, the Secant method, and the NewtonSecant method that has not been modified. The obtained results from the construction of mathematical model NewtonSecant method and its modification is an iteration formula modification of NewtonSecant method. And for the result of f(x) using a modification of NewtonSecant method with four different initial guess, the root of x is obtained approximately, namely 0.641714371 with fewer iterations if compared to using the Newton method, the Secant method, and the NewtonSecant method. Based on the problem to find the root of the nonlinear equation f(x) it can be concluded that the modification of NewtonSecant method is more effective than the Newton method, the Secant method, and the NewtonSecant method
Item Type:  Journal Article 

Keywords:  modification; NewtonSecant method; nonlinear equation; multiple zeros; trigonometric function 
Subjects:  01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics 
Divisions:  Faculty of Mathematics and Sciences > Department of Mathematics 
Depositing User:  Juhari Juhari 
Date Deposited:  12 Nov 2021 13:17 
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