scholarly journals Perbandingan Metode Newton-Raphson & Metode Secant Untuk Mencari Akar Persamaan Dalam Sistem Persamaan Non-Linier

Petir ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 72-79
Author(s):  
Endang Sunandar ◽  
Indrianto Indrianto

The numerical method is a technique used to formulate mathematical problems so that it can be solved using ordinary arithmetic operations. In general, numerical methods are used to solve mathematical problems that cannot be solved by ordinary analytic methods. In the Numerical Method, we recognize two types of systems of equations, namely the Linear Equation System and the Non-Linear Equation System. Each system of equations has several methods. In the Linear Equation System between methods is the Gauss Elimination method, the Gauss-Jordan Elimination method, the LU (Lower-Upper) Decomposition method. And for Non-Linear Equation Systems between the methods are the Bisection method, the Regula Falsi method, the Newton Raphson method, the Secant method, and the Fix Iteration method. In this study, researchers are interested in analyzing 2 methods in the Non-Linear Equation System, the Newton-Raphson method and the Secant method. And this analysis process uses the Java programming language tools, this is to facilitate the analysis of method completion algorithm, and monitoring in terms of execution time and analysis of output results. So we can clearly know the difference between what happens between the two methods.

Petir ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 179-186
Author(s):  
Endang Sunandar

The numerical method is a technique used to formulate mathematical problems so that they can be solved using ordinary arithmetic operations. In general, numerical methods are used to solve mathematical problems that cannot be solved by ordinary analytical methods. In the Numerical Method, we know two types of system equations, namely the Linear Equation System and the Non-Linear Equation System. Each system of equations has several methods. In the System, the Linear Equation between the methods is the Gauss Elimination method, the Gauss-Jordan Elimination method, the LU (Lower-Upper) Decomposition method. And for the Non-Linear Equation System between the methods is the Bisection method (Share-Two), Falsi Regula method, Newton Raphson method, Secant method, and Fix Iteration method. In this study, researchers are interested in comparing the two methods in the Non-Linear Equation System, namely the Bisection method and the Falsi Regula method. And this benchmarking process uses the Java programming language tool, this is to facilitate analysis of method completion algorithms, and monitoring in terms of execution time and output analysis. So that we can clearly know what differences occur between the two methods.


2019 ◽  
Vol 19 (1) ◽  
pp. 29
Author(s):  
Ana Ulul Azmi ◽  
Rusli Hidayat ◽  
M Ziaul Arif

Non-linear equation system is one of the mathematics problems which difficult to solve. Several methods have been introduced to solve the problems. Newton-Raphson method is the most common and widely used as the basis for evolving the latest numerical methods. However, this method requires the derivative of each equation with respect to every variable when calculating the Jacobian. Naturally, obtaining the derivative is challenging in certain cases. In addition, it needs a proper initial value to obtain the converged solution. Therefore, the new technique with a simple random initial value is urgently needed. In this study, it is shown the implementation of the two metaheuristic optimization methods, including Particle Swarm Optimization (PSO) and the Glowworm Swarm Optimization (GSO) to estimate the solution of a non-linear equation system. Several examples of nonlinear equation system were used for evaluating and testing the performance and the accuracy of both algorithms. In this simulation, the results show that PSO converged to the exact solution (global optimum) better than Glowworm Swarm Optimization (GSO). Keywords: Non-Linear Equation Systems, Particle Swarm Optimization (PSO), Glowworm Swarm Optimization (GSO)


2016 ◽  
Vol 11 (1) ◽  
pp. 136-140
Author(s):  
D.M. Zaripov

The non-linear bend of flight of the horizontal pipeline on two support under the influence of impact pressure in internal liquid with taking note of longitudinal force on a bend is considered. The solution of the non-linear equation of the task is received by the numerical method. Comparing of results is given in the linear and non-linear settings. It is shown that in a non-linear case there is an oscillatory mode of movement of the pipeline, in difference from the linear case when there is an exponential growth of amplitude of a bending of the pipeline.


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