Numerical methods
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The document discusses several numerical methods for finding roots of equations, including the bisection method, false position method, Newton's method, and secant method. It provides examples of using each method to solve equations like x - cos(x) = 0 and x^3 - x - 1 = 0. The document concludes by listing references used in explaining these numerical root-finding techniques.
Numerical methods
- 1. By Ahmed Haider Ahmed Pre-M.Sc. Physics – ASU
- 2. To My father , May Allah enter you his paradise
- 3. 1 – Bisection Method If F(wi+1) is negative we put wi+1 instead of ai or bi 2 1 ii i ba w
- 4. 2 – Falsie Method )()( )()( 1 ii iiii i bfaf afbbfa x
- 5. 3 – Newton Method )( )( 1 i i ii xf xf xx
- 6. 4 – Secant Method )()( ))(( 1 1 1 ii iii ii xfxf xxxf xx
- 7. Examples
- 8. Find the positive root of x – cos x = 0 using bisection method. We will take points that give positive value with the negative one i.e 0 and 1 )(1)2( )(00015.0)1( )(1)0( cos)( vef vef vef xxxf
- 9. )(249.0)75.0( 75.0 2 15.0 150 )(5.0)5.0( )(5.0 2 10 10 2 1 vef x and.enroot betweHence the vef vex andenroot betweHence the
- 10. 062.0)9375.0( 9375.0 2 1875.0 18750 )(12488.0)875.0( 875.0 2 75.01 1750 4 3 f x and.enroot betweHence the vef x and.enroot betweHence the
- 11. Solve equation x3 – x – 1 = 0 using falsie method. 5128)2( 1111)1( 1)( 3 f f xxxf 2,1 )()( )()( 00 00 0000 1 ba bfaf afbbfa x
- 15. Solve equation x3 – x – 1 = 0 using Newton method at x0 = 1 213)( 1111)( 13)( 1)( )( )( 0 0 2 3 1 xf xf xxf xxxf xf xf xx i i ii
- 18. REFERANCES Lecture notes on numerical methods , Dr. Shemi 2011, Minia university written by Aya Hassan. Lecture notes on computational physics for Pre-M.Sc. Students , Prof. Dr. S.Hendawi 2013, Ain Shams University.