The Newton-Raphson method is said to have

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MPSC AE CE Mains 2017 Official (Paper 1)

Option 3 : Quadratic convergence

**Concept:**

Newton- Raphson method:

- The Newton - Raphson method is the type of open method (
**Extrapolation method)**. - It is a powerful technique for
**solving algebraic and transcendental equations**f( x ) = 0, numerically. - It is an iteration method for solving a set of various nonlinear equations with an equal number of unknowns.

Advantages:

- It possesses
**quadratic convergence characteristics**. Therefore, the convergence is very fast. - The number of iterations is independent of the size of the system.
- The Newton-Raphson Method convergence is not sensitive to the choice of slack bus.
- Overall, there is a saving in computation time since a fewer number of iterations are required.

Disadvantages:

- It does not converge to a root when the second differential coefficient changes sign

- It is sensitive to the starting value. Convergence fails if the starting point is not near the root.
- It is not preferred when the graph of f(x) is nearly horizontal where it crosses the x-axis as the values of f’(x) have negative values in this case.