Why does it not do this for negative values as well? Here is my updated code: program bisec IMPLICIT NONE REAL(10):: a, b, m, f_xa, f_xb, f_xm, pi INTEGER:: i, n WRITE (*,*) 'LAB 5- Bisection Method' WRITE (*,*) '-' WRITE (*,*) ' ' WRITE (*,*) 'Please enter the interval :' READ (*,*) a,b pi = 3.1415926 DO i = 0, 1000 m = (a + b)/2. When evaluating for positive values however, no matter what the order of the numbers, it displays the correct solution. The problem I seem to be having with negative intervals though is that when I punch in evaluate from it will display -7 as a solution, however if I enter it as it will display -8 as the correct solution. I thought about testing end points too, the program seems to work fine for positive and negative values where one of the limits (A or B) is actually the solution. I wound up initializing m inside the do loop, so it's initial value is the result of the operations on A and B, and it updates through each iteration. You're right, I'm not sure why on earth I was test m instead of f_xm for the condition, but I've fixed that. I made some modifications last night, after I posted actually. This may cause you grief (like an infinite loop for some pairs ). I note that you don't do any preliminary testing to see that the interval actually contains a zero. Surely if you're looking for a root you want the value of the function f(m) to approach zero, not the value of m m is simply the midpoint x-value, which takes on values in your search interval. What is the value of m the first time the DO condition is tested (that is, what is its value just prior to entering the DO loop for the first time? F_xa = SIN(a) f_xb = SIN(b) f_xm = SIN(m) IF (ABS(m) 0) THEN a= m ELSE IF (f_xa*f_xm. The attempt at a solution program bisec IMPLICIT NONE REAL:: a, b, m, f_xa, f_xb, f_xm WRITE (*,*) 'Please enter the interval :' READ (*,*) a,b DO!WHILE (ABS(m) >1E-7) m = (a + b)/2.
The intervals are input by the user, and then the do loop continues until the condition (m becomes very close to 0 or equals 0) is met. The problem statement, all variables and given/known data The purpose of this program is to calculate the approximate roots of the Sine function on given intervals. In the following table, each line/entry contains the program file name, the page number where it can be found in the textbook, and a brief description.
Lagrange interpolation with the Aitken method (appeared in the book). This method is used to find root of an equation in a given interval that is value of ‘x’ for which f(x) = 0. What is Bisection Method? The method is also called the interval halving method, the binary search method or the dichotomy method.
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