Script to solve quadratic - help

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  • Thread starter Thread starter mklein
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Discussion Overview

The discussion revolves around writing a JavaScript script to calculate the roots of a quadratic equation using the Bisection Method. Participants explore the implementation details, the method's reliability, and the motivations behind writing custom code versus using existing solutions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Meta-discussion

Main Points Raised

  • Matt expresses frustration with a script that previously worked but now fails to converge when calculating the root of a quadratic equation.
  • Integral identifies that Matt is using the Bisection Method and suggests a necessary condition for the method to work: the product of the function values at the endpoints must be negative.
  • Integral recommends checking the midpoint against the function values to update the interval correctly.
  • Matt appreciates the identification of the method and expresses interest in looking up examples online.
  • Duncan questions the choice of using the Bisection Method and suggests that there are existing scripts available online.
  • Matt responds that he is revisiting coding for personal reasons and acknowledges his background as an A-level physics teacher, indicating that coding is not his primary focus.

Areas of Agreement / Disagreement

Participants generally agree on the use of the Bisection Method and its requirements, but there is no consensus on why Matt chose to write his own script instead of using existing solutions. The discussion remains open regarding the effectiveness of the current implementation.

Contextual Notes

Matt's script does not converge, and there are unresolved issues regarding the initial conditions and the implementation of the Bisection Method. The discussion does not clarify whether the method is being applied correctly in all cases.

Who May Find This Useful

Individuals interested in numerical methods for solving equations, JavaScript programming, or those revisiting coding after a break may find this discussion relevant.

mklein
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Dear forum

Please help - I am feeling very useless and depressed as something which worked years ago while at uni now seems to beat me !

I am trying to write a simple script (javascript actually) which calculates the root of a quadratic given two guesses of x (one guess giving y<0, the other giving y>0). From these values of x1 and x2 it calulates y at the mid-point, and depending on whether y is positive or negative it moves one of the boundaries half-way towards the midpoint.

I will paste the code below. The program runs but doesn't converge:

<html>
<body>
<script type="text/javascript">
document.write("Solving the equation : 3x^2-5=0");
x1 = window.prompt ("Enter a VERY LOW initial guess for x");
x2 = window.prompt ("Now enter a VERY HIGH initial guess for x");
x=(x1+x2)/2;
y=3*x^2-5;
document.write(y);

while (Math.abs(y) >= 0.01)
{

if(y<0)
{x1=(x+x1)/2;
}

else if(y>0)
{x2=(x+x2)/2;
}

x=(x1+x2)/2;
y=3*x^2-5;

document.write(x1);
document.write(x2);
document.write(y);
}
</script>
</body>
</html>


I realize there are probably better ways of acheiving the same thing, but I'm sure this (or something very similar) used to work.

Thank you in anticipation

Matt Klein
 
Physics news on Phys.org
You are doing a simple bisection medthod, not the fastest method, certianly a reliable one.

You need to start with a check that you indeed have a root on your initial interval.

so: [tex]f(x_1) * f(x_2) <0[/tex] has to be true before you start the procedure.
if xm is your mid point.

check if [tex]f(x_1) * f(x_m) >0[/tex] if true let [tex]x_1 = x _m[/tex]

if false let [tex]x_2 = x_m[/tex]

repeat until f(xm) is sufficient small.
 
Thanks for your reply Integral

It was especially useful to know the methods name (Bisection Method) as now I can look up all sorts of simple examples elsewhere on the net

Cheers

Matt
 
I am curious: why are you using the Bisection Method? And why are you writing your own script instead of using one of the many already available on the Internet?
 
Hi Duncan

Just for the sake of it really. It is some years since I wrote any code. Of course I could solve this sort of quadratic in seconds, but I wanted to revisit the bisection method and see if I could make it work!

I am an A-level physics teacher so coding is not the sort of thing I would normally get round to doing

Matt
 

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