A Modified Secant Method for Solving Nonlinear Equations
Abstract
In this research, we propose a modification of the Classical Secant method for solving nonlinear equations in the form of. The Divided Difference is applied into the Secant method and now the iterative algorithm depended on two initial points. We conduct numerical simulations to compare our modified method with Newton and the original one, in which the number of iterations, the computational order of convergence (COC) and graphs of relative error of each are implemented. There are three test functions i.e., ,and . The numerical results show that the modified method have the number of iteration and the rate of convergence similar to Newton method. Keywords : nonlinear equations, Newton method, Secant method, iterative methodReferences
Allame, M. and Azad, N. (2012). On Modified Newton Method for Solving a Nonlinear Algebraic Equations by Mid-Point. World Applied Sciences Journal, 17(12), 1546-1548.
Babolian, E. and Biazar, J. (2002). On the order of convergence of Adomian Method. Applied Mathematics and Computation, 130, 383-387.
Ide, N. (2008). A new Hybrid iteration method for solving algebraic equations. Applied Mathematics and Computation, 195, 772-774.
Srivastava, R.B. and Srivastava, S. (2011). Comparison of Numerical Rate of Convergence of Bisection, Newton and Secant Methods. Journal of Chemical Biological and Physical Sciences, 2(1), 472-479.
Traub, J. F. (1964). Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs, N.J.
Babolian, E. and Biazar, J. (2002). On the order of convergence of Adomian Method. Applied Mathematics and Computation, 130, 383-387.
Ide, N. (2008). A new Hybrid iteration method for solving algebraic equations. Applied Mathematics and Computation, 195, 772-774.
Srivastava, R.B. and Srivastava, S. (2011). Comparison of Numerical Rate of Convergence of Bisection, Newton and Secant Methods. Journal of Chemical Biological and Physical Sciences, 2(1), 472-479.
Traub, J. F. (1964). Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs, N.J.
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2017-07-26
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บทความวิจัยจากการประชุมวิชาการระดับชาติ"วิทยาศาสตร์วิจัย"ครั้งที่ 9
