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Lecture_09_Newton-Raphson_Method

# Lecture_09_Newton-Raphson_Method - EGR 102 Introduction to...

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EGR 102 Introduction to Engineering Modeling Newton-Raphson Method hapter 6.1- .2 Chapter 6.1 6.2 EGR 102 Lecture 9 1 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill

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Objectives Know the difference between bracketing and open methods for root location. Learn how to solve a roots problem with the Newton- Raphson method and understand the concept of quadratic convergence. Learn how to use MATLAB’s fzero function to estimate roots. earn how to manipulate and determine the ots f Learn how to manipulate and determine the roots of polynomials with MATLAB. EGR 102 Lecture 9 2
Roots ± Roots of an equation: ± Values of x that make ƒ(x) = 0 ± Also called “zeros” of the equation EGR 102 Lecture 9 3

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erative Root Solving onlinear Equation Iterative Root Solving Nonlinear Equation Solvers Bracketing Graphical Open Methods Bisection Newton-Raphson EGR 102 Lecture 9 4
Open Methods Open methods differ from bracketing methods, in that open methods require only a single starting value or two starting values that do not necessarily bracket a root. may diverge as the computation rogresses but when they do converge they usually do so progresses, but when they do converge, they usually do so much faster than bracketing methods. are based on formulas that require only a single starting value of x or two starting values that do not necessarily bracket the root. EGR 102 Lecture 9 5

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Graphical Comparison of Methods a) Bracketing (bisection) method where the root is constrained within the interval ounded by nd bounded by x l and x u b)Diverging open (Newton-Raphson)
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Lecture_09_Newton-Raphson_Method - EGR 102 Introduction to...

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