Bisection method in fortran 90

jhosamelly

Bisection method for the equation x3−2x−2 = 0 which has a single root
between x=−4 and x = 2.

here's the code I have

I know there's something wrong with my code. Can somebody help me please?

Here are the Bisection Method formulas

xm = (xl+xu)/2

uart

The code at the line starting: "if fxnew>0 then" can never execute. Take a close look and see if you can tell me why?

A couple of other points.
1. Even if you fix the above problem, your code may never terminate. Requiring exact (FP) equality with zero is a bad idea.
2. There's no real reason to use to goto in this code. You should look at alternative methods of program flow control.
3. It will really help you keep track of your code if you start making use of indentation.

jhosamelly

I'm guessing coz there is no "end if"?

I don't know. sorry.. How can I do the iteration here?

Thanks for the help

uart

Yes, unless you use "end if" then the statement "if fxnew>0 then" is still under the control if the previous "if".

I'm surprised that the program even compiled without the "end if" statements. (BTW. does it actually compile?)

jhosamelly

Can you please please help me? How can I put the conditions above and do the iteration? Please? thanks.

Yes it did compile.

uart

Yes there's still quite a few thing wrong with code, but you know we can't write your program for you. :)

I'll look at one section:
You're kind of got the right idea. This section is executed if xnew is opposite sign to xlow, so you now know the zero crossing is between xlow and xnew. Now you want to let xnew become the new xhigh, and keep xlow as is. Can you see that of your two assignment statements, one is redundant and the other is the wrong way around.

TheoMcCloskey

... and don't forget to correct your inital conditions.

jhosamelly

Ow. So it should be

xl=xl
xu=xnew

Correct? Then? What should I do?

uart

Take all the advice and hints you've been given so far then sit down and write a new iteration of your program.

SteamKing

xl = xl is redundant

jhosamelly

hmmm.. yes. But how can I put that xl=xl and use it on the equation again in program?

just give me one example and i'll do it for the rest of the statements. Thanks. I really don't have any idea.

Mark44

It's silly and a waste of time to set a variable to its own value.

You're doing the same thing later in your program where you set xu = xu.

What is your purpose in doing this?

jhosamelly

I need to put in codes the conditions given.

Mark44

I'm not convinced that you understand what the above means.

x_L - Lower (left) endpoint of an interval
x_M - Midpoint of an interval
x_U - Upper (right) endpoint of an interval

a) If f(x_L)*f(x_M) < 0, the graph of the function crosses the x-axis somewhere between x_L and x_M, so the root you're looking for must be in the left half of the original interval. If so, USE THE SAME VALUE FOR x_L (i.e., don't change x_L) but reset x_U to x_M. Your code should NOT include x_L = x_L.

b) If f(x_L)*f(x_M) > 0, the graph of the function does not cross the x-axis between x_L and x_M, so we should look in the other half of the interval - in [x_M, x_U]. If so, USE THE SAME VALUE FOR x_U (i.e., don't change x_U), but reset x_L to x_M. Your code should NOT include x_U = x_U.

At each step for a) or b), we are shortening the interval by half its length, so that we eventually find the root.

c) If f(x_L)*f(x_M) = 0 then either f(x_L) = 0 or f(x_M). There's probably an assumption that f(x_L) ≠ 0 and f(x_U) ≠ 0, but you didn't show it in the attachment you posted.

jhosamelly

Yes, I understand that,, I just dont know how to put it in codes. i'll work on all your hints now. Thanks :)

Integral

Perhaps you could work through several iterations by hand. Once you get an understanding of how the algorithm works you can then write the code.

Step 1. Is there a root on the interval?
Step 2. Find the midpoint.
step 3. Find the half that has a root.
Step 4. Repeat.

jhosamelly

I did that already. Im not getting the same answer with the the program so I know there's something wrong. Thanks for the help guys. Appreciate it.