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The main disadvantage of the bisection method for finding the root of an equation is that, compared to methods like the Newton-Raphson method and the Secant method, it requires a lot of work and a lot of iterations to get an answer with very small error, whilst a quarter of the same amount of work on the N-R method would give an answer with an error just as small.

In other words compared to other methods, the bisection method takes a long time to get to a decent answer and this is it's biggest disadvantage.

Q: Disadvantages of the bisection method in numerical methods?

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A root-finding algorithm is a numerical method, or algorithm, for finding a value. Finding a root of f(x) − g(x) = 0 is the same as solving the equation f(x) = g(x).

Numerical methods are used to find solutions to problems when purely analytical methods fail.

To know which numerical method to use for a problem one first needs to understand the various methods and evaluate the problems.

Yes, you can. Any iterative method/algorithm that is used to solve a continuous mathematics problem can also be called a numerical method/algorithm.

In the absence of other information, it is the most efficient.

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A root-finding algorithm is a numerical method, or algorithm, for finding a value. Finding a root of f(x) − g(x) = 0 is the same as solving the equation f(x) = g(x).

Numerical methods are used to find solutions to problems when purely analytical methods fail.

To know which numerical method to use for a problem one first needs to understand the various methods and evaluate the problems.

There are to classes of methods to find the minimum of a function: analytical and numerical. Analytical methods are precise but cannot be applied always. For example, we can find the minimum of a function by setting its first derivative to zero and solve for the variable and then check the second derivative (must be positive). Numerical methods involve the application of steps repeatedly until an acceptable estimate of the solution is found. Numerical methods include Newton method, steepest descent method, golden section method, Simplex method, to name just a few.

Yes, you can. Any iterative method/algorithm that is used to solve a continuous mathematics problem can also be called a numerical method/algorithm.

In the absence of other information, it is the most efficient.

The Runge-Kutta method is one of several numerical methods of solving differential equations. Some systems motion or process may be governed by differential equations which are difficult to impossible to solve with emperical methods. This is where numerical methods allow us to predict the motion, without having to solve the actual equation.

1. it is always convergent. 2. it is easy

The rate of convergance for the bisection method is the same as it is for every other iteration method, please see the related question for more info. The actual specific 'rate' depends entirely on what your iteration equation is and will vary from problem to problem. As for the order of convergance for the bisection method, if I remember correctly it has linear convergence i.e. the convergence is of order 1. Anyway, please see the related question.

Irwin Remson has written: 'Numerical methods in subsurface hydrology, with an introduction to the finite element method' -- subject(s): Groundwater, Numerical analysis

The bisection method is simpler to implement and guarantees convergence to a root if one exists within the initial interval, but it can be slower as it always halves the interval. In contrast, linear interpolation converges faster but does not guarantee convergence, and it might fail if the function is not well approximated by a linear model in the interval.

The root of f(x)=(1-0.6x)/x is 1.6666... To see how the bisection method is used please see the related question below (link).