CH ENGR 109 Study Guide - Quiz Guide: Mazda E Engine, Euler Method, Trigonometric Functions
Document Summary
Cbe 109 - numerical and mathematical methods in chemical and biological engineering. From taylor series, we have f (xroot) = f (x(m)) + df dx (x(m))(xroot x(m)) + 2 d2f dx2 (x(m))(xroot x(m))2 + o((xroot x(m))3) = 0. 2 d2f dx2 (x(m)) df dx (x(m)) c = f (x(m)) X(m) = x(m+1) x(m) then we have a( x(m))2 + b x(m) + c = 0 (1) When the initial guess is close enough to the true root, equation 1 has two real roots. x = b . To start the iteration, rst use newton"s method to calculate x(1) of equation 1 that is closer to x(1) closer to the previous one. newton and then keep the root newton. In the following iterations, always use the root that is: recall the basic result on the rate of convergence for the newton-raphson method: ]2 which holds in the vicinity of the root xr.
