# On the modification of newton-secant method in solving nonlinear equations for multiple zeros of trigonometric function

Juhari, Juhari (2021) On the modification of newton-secant method in solving nonlinear equations for multiple zeros of trigonometric function. Cauchy: Jurnal Matematika Murni dan Aplikasi, 7 (1). pp. 84-96. ISSN 2086-0382

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## Abstract

This study discusses the construction of mathematical model modification of Newton-Secant method and solving nonlinear equations for multiple zeros by using a modified Newton-Secant 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 Newton-Secant method and its modification, 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 θ. After obtaining the formula for the modification Newton-Secant 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^2⁡x+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 Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified. The obtained results from the construction of mathematical model Newton-Secant method and its modification is an iteration formula modification of Newton-Secant method. And for the result of f(x) using a modification of Newton-Secant 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 Newton-Secant method. Based on the problem to find the root of the nonlinear equation f(x) it can be concluded that the modification of Newton-Secant method is more effective than the Newton method, the Secant method, and the Newton-Secant method

Item Type: Journal Article modification; Newton-Secant method; nonlinear equation; multiple zeros; trigonometric function 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics Faculty of Mathematics and Sciences > Department of Mathematics Juhari Juhari 12 Nov 2021 13:17