Page 531 - Modelling in Transport Phenomena A Conceptual Approach

A.7. THE ROOT OF AN EQUATION 511

Figure A.3 The Newton-Raphson method.

To evaluate the derivative in Eq. (A.7-18), linear interpolation between two
points, zk and zk-1, on the function is applied in the form

- (A. 7- 19)
dx 51: Zk - Zk-1
Substitution of Eq. (A.7-19) into Eq. (A.7-18) gives

(A.7-20)

Note that the secant method requires two initial guesses. The secant method is
illustrated in Figure A.4.

Figure A.4 The Secant method.