This is a program which uses the bisection method to approximate roots of an equation f(x)=0. The input consists of an equation for the function f(x) and values a and b for which f(a) and f(b) have opposite signs. (In the program, we test whether f(a) and f(b) have opposite signs by checking whether the product f(a)f(b) is negative). The program then checks the midpoint c of a and b to determine whether f(c) is opposite in sign to f(a) or to f(b). In the first case, b is replaced by c, while in the second a is replaced by c. At this point, the program prints out the current value of a (which represents an approximation to the root) and of b-a (which represents the accuracy of the approximation). The process is then repeated in an unending loop.

Here is the code (suitable for the TI-85).

:Disp "This program uses"
:Disp "the bisection method"
:Disp "to approximate a"
:Disp "root of f(x)=0 given"
:Disp "x-values a and b"
:Disp "where f(a)f(b)<0."
:Disp "Press enter to continue"
:Pause
:Disp ""
:
:InpSt "f(x)= ",f
:St>Eq(f,F)
:Input "a= ",A
:Input "b= ",B
:
:Lbl HERE
:.5*(A+B)->C
:evalF(F,x,A)->FA
:evalF(F,x,C)->FC
:
:If FA*FC>0
:Then 
:C->A
:Else
:C->B
:End
:
:Disp "There is a root at ",A
:Disp "accurate to within ",B-A
:Disp ""
:Pause
:
:Goto HERE

[In the code typed above, the symbols "St>Eq(" and "evalF(" can be found on the CATALOG menu. The symbol "->" is accessed using the "STO>" key which is the second key from the lefthand bottom of the calculator. Many of the other command words can be found on the I/O and CTL menus. The greater than and less than symbols may be found on the TEST menu.]

This document was created in November 1996 
and last revised on August 15, 1998.