Lecture05 - Solutions of Nonlinear Equations and Systems of...

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1 Solutions of Nonlinear Equations and Systems of Equations •Why? •But a ac b b x c bx ax 2 4 0 2 2 ! ! = " = + + m ? 0 sin ? 0 2 3 4 5 = ! = + = ! = + + + + + x x x x f ex dx cx bx ax Nonlinear Equation Solvers Bracketing Graphical Open Methods Bisection False Position (Regula-Falsi ) Newton Raphson Secant All Iterative Bracketing Methods (Or, two point methods for finding roots) • Two initial guesses for the root are required. These guesses must “bracket” or be on either side of the root Read Graphical Methods Sec. 5.2 If one root of a real and continuous function, f(x)=0, is bounded by values x=x l , x =x u then f(x l ) . f(x u ) <0. The function changes sign on opposite sides of the roo Graphical Methods Fig 5.4a
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2 Fig 5.4c The Bisection Method For the arbitrary equation of one variable, f(x)=0 1. Pick x l and x u such that they bound the root of interest, check if f(x l ).f(x u ) <0. 2. Estimate the root by evaluating f[(x
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This note was uploaded on 03/20/2010 for the course CHEN 313 taught by Professor Seminario during the Spring '07 term at Texas A&M.

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Lecture05 - Solutions of Nonlinear Equations and Systems of...

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