Lecture-3-2-Roots of Equations-slides

Lecture-3-2-Roots of Equations-slides - BME 5020 Computer...

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BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Roots of Equations BME 5020 Computer and Mathematical Application in Bioengineering © 2006 Jingwen Hu September 21, 2006 • Bracketing Methods • Open Methods • Case study Contents
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Introduction BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University 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 •W h y ? •B u t
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Introduction BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Nonlinear Equation Solvers Bracketing Graphical Open Methods Bisection False Position (Regula-Falsi ) Newton Raphson Secant
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Graphical Methods • A simple methods for obtaining an estimate of the root of the equation f(x)=0 is to make a plot of the function and observe where it crosses the x axis. BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University
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Graphical Methods BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University x x x F 3 cos 10 sin ) ( + =
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Graphical Methods • Determine c when m=68.1kg, v=40m/s, and t=10s . BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University ( ) t m c e c gm t v ) / ( 1 ) ( = ( ) 10 ) 1 . 68 / ( 1 1 . 68 * 8 . 9 40 c e c = ( ) 40 1 1 . 68 * 8 . 9 ) ( 10 ) 1 . 68 / ( = c e c c F ( ) 40 1 38 . 667 ) ( 146843 . 0 = c e c c F
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Graphical Methods • Determine c when m=68.1kg, v=40m/s, and t=10s . BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University () 40 1 38 . 667 ) ( 146843 . 0 = c e c c F -8.401 20 -2.269 16 6.067 12 17.653 8 34.115 4 f(c) c
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Bisection Method BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University
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Bisection Method BME5020 2006, Fall Semester |Biomedical Engineering, Wayne State University Step4: Estimate the approximate percent relative error Step 5: Compare ε s with ε a. If ε a < ε s, stop. Otherwise repeat the process. % 100 new r old r new r a x x x = ε
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