mase201sp09_Mar31_PRINTABLE - Finding zeros of nonlinear...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Finding zeros of nonlinear functions ackground nd pproaches • Background and approaches • Bisection method (bracketed interval) • Newton’s method (open interval with analytic derivative) ecant method (open interval with • Secant method (open interval with approximate derivative) ATLAB built functions zero ec 10 1 • MATLAB built-in functions fzero (sec 10.1 in your text) 3/31/2009 1 MASE201 Spring 2009 Review our example For a given applied F , coefficient of iction and mass find t friction , and mass m , find at which the block will start to move Solution method: g m F The sliding block – Guess –C a l c u l a t e F using equation ompare to applied F Compare to applied – Adjust to reduce error between calculated and applied F equires repeated calculation of g m Requires repeated calculation of cos and sin functions sin cos F 3/31/2009 2 MASE201 Spring 2009 Problem Solution Method? sin cos g m F What’s a good starting guess for ? Divide F by mg Consider limiting cases: = 0 or 90 deg sin cos g m F 1 0 n s 0 90 sin cos 3/31/2009 3 MASE201 Spring 2009 Problem Approach (cont’d) • We can plot solution at g m specific values of • The shape of the F - curve hanges for each value of sin cos F changes for each value of • There may be 0, 1, or 2 solutions for depending upon the ratio F/(mg) and 3/31/2009 4 MASE201 Spring 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Finding f(x) = 0 ifferent possibilities for number of solutions • Different possibilities for number of solutions (roots): x) 0 f( x 0 0 0 No solution One solution One solution Several solutions x x x x 3/31/2009 5 MASE201 Spring 2009 Approach Make an initial estimate for the numeric solution Bracketing Methods pen Methods (approximate solution) Use the approximate solution to find a better Open Methods numeric solution Stop when the solution is precise enough 3/31/2009 6 MASE201 Spring 2009 Figure 3-5 from Gilat, “Numerical Methods for Engineers and Scientists” Bracketing and Open Methods • Bracketing Methods – Will converge to a solution • Open Methods – May not find a solution – May be less efficient • We will discuss: isection method – May require fewer iterations e will discuss: – Bisection method • Other methods: Regula falsi method We will discuss: – Newton’s method – Secant method
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 05/05/2010.

Page1 / 5

mase201sp09_Mar31_PRINTABLE - Finding zeros of nonlinear...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online