Write a program using Bisection method and method of false position.

[DaisyShafi]

Hello everyone.
I'm new here and I'm not not a computer science student.
But, I have to take programming to complete my degree.
So, now I'm in a great depression about this assignment.
My lecturer ask me to write a program to find root of an equation f(x)=0 for specific f. Both methods are need to be in my assignment.
So, where should I start?

 

[jfgobin]

Hello DaisyShafi,

First, write your two methods using pseudo code.

What language do you need to use?

J.

 

[DaisyShafi]

What language ? English.
Can you show me the step?
Do I need to include the f(x) polynomial equation into the coding?

 

[jfgobin]

What computer language?

Pseudo code is writing something like:

for the integer n given as an argument:
while n > 0 do
     n <- n -1

 

[rezeew]

Hello, welcome to the world of programming! Don't worry, even if you are not a computer science student, you can still learn and write programs. Let's start with understanding the Bisection method and the method of false position.

The Bisection method is a numerical method for finding the root of a function by repeatedly bisecting an interval and determining which subinterval contains the root. This method is based on the intermediate value theorem, which states that if a continuous function takes on positive and negative values at two points, then it must also take on the value of zero at some point in between.

The method of false position, also known as the regula falsi method, is similar to the Bisection method but instead of bisecting the interval, it approximates the root by finding the intersection of the line connecting the two function values at the endpoints of the interval. This method is faster than the Bisection method but may not always converge to the root.

Now, for your assignment, you can start by understanding the algorithm for both methods and then translating it into code. You can use any programming language of your choice. Here are some steps to get you started:

1. Define the function f(x) that you want to find the root for.
2. Choose an initial interval [a,b] such that f(a) and f(b) have opposite signs.
3. Implement the Bisection method:
a. Calculate the midpoint c = (a+b)/2
b. If f(c) = 0, then c is the root.
c. If f(a) and f(c) have opposite signs, then the root lies in the interval [a,c].
d. If f(b) and f(c) have opposite signs, then the root lies in the interval [c,b].
e. Repeat steps a-d until the desired accuracy is reached.

4. Implement the method of false position:
a. Calculate the slope of the line connecting (a,f(a)) and (b,f(b)).
b. Find the x-intercept of this line.
c. If f(x-intercept) = 0, then the x-intercept is the root.
d. If f(a) and f(x-intercept) have opposite signs, then the root lies in the interval [a,x-intercept].
e. If