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Chapter-05 - Solutions of Nonlinear Equations and Systems...

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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 = = + = = + + + + + ξ ξ ξ ξ φ εξ δξ χξ βξ αξ
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Nonlinear Equation Solvers Bracketing Graphical Open Methods Bisection False Position (Regula-Falsi ) Newton Raphson Secant All Iterative
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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 o Read Graphical Methods Sec. 5.1 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
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Graphical Methods
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Fig 5.4a
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Fig 5.4b
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Fig 5.4c
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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. 1. Estimate the root by evaluating f[(x l +x u )/2].
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