Solving Equation with Bisection Method - Real Root Between -2*pi and 2*pi

In summary, the bisection method is a numerical root-finding algorithm that works by repeatedly dividing an interval in half to find the root of an equation. To use this method, one must first identify an interval with opposite signs at the endpoints and then continue dividing until a small enough interval is reached. The bisection method can be used for any continuous function, but is most effective when the function is monotonic within the chosen interval. This method can only find real roots and has the advantages of being simple, guaranteed to converge, and not affected by initial guesses.
  • #1
jrm2002
57
0
I need to solve this equaation:

(x1cos(p)+y1sin(p))^2 * (x2sin(p)-y2cos(p)) = (x1sin(p)-y1cos(p)) * (x2cos(p)+y2sin(p))^2 ;

x1,x2,y1,y2 are constants

The equation would have 3 roots

1 real and two imaginary

I don't need imaginary roots.

I am planning to use bisection method-----

since i know the real root will lie between -2*pi and 2*pi

What is your comment on this?
 
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  • #2
Without commenting on your method I see that the equation as stated doesn't make sense. You have unbalanced parentheses on both sides.
 

1. What is the bisection method and how does it work?

The bisection method is a numerical root-finding algorithm used to solve equations. It works by repeatedly dividing the interval of interest in half and checking which half contains the root. The process continues until the interval is small enough to approximate the root.

2. How do you use the bisection method to solve an equation?

To use the bisection method, you first need to identify an interval in which the root is located. Then, you need to choose two points within that interval and evaluate the function at those points. If the function has opposite signs at the two points, the root is between them. You can then divide the interval in half and repeat the process until you have a small enough interval to approximate the root.

3. What is the range of values for the bisection method to work?

The bisection method can be used to find real roots for any continuous function. However, it is most effective when the function is monotonic (always increasing or always decreasing) within the interval of interest. In this case, the interval should be chosen so that the function has opposite signs at the endpoints.

4. Can the bisection method find complex roots?

No, the bisection method is only applicable for finding real roots. It cannot find complex roots, which require different numerical methods.

5. What are the advantages of using the bisection method?

The bisection method is simple and easy to implement. It is also guaranteed to converge to a solution as long as the function is continuous and has opposite signs at the endpoints of the chosen interval. Additionally, it can handle a wide range of functions and is not affected by initial guesses.

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