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Lecture05

# 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 l +x u )/2]. 3. Find the pair If f(x l ). f[(x l +x u )/2]<0, root lies in the lower interval, then x u =(x l +x u )/2 and go to step 2.
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Lecture05 - Solutions of Nonlinear Equations and Systems of...

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