### Numerical Methods - The Newton-Raphson Method to Solve Mechanical Design Problems Part I

Machine designers have to deal with several number of equations in their design projects. There are a number of ways to solve for roots of algebraic and transcendental equations. Sometimes, the roots could be obtained by direct methods. However, there are many more that could not. The classical equation such as f(x) = e-x - x cannot be solved analytically. For this case, the only alternative is an approximate solution technique.

There are several methods available to solve the root finding problem such as "bracketing methods" and "Open methods".

The bracketing methods require 2 initial guesses for the root. These guesses must "bracket" the root. The numerical methods using bracketing methods consist of the following techniques:

The Bisection Method: The idea of this technique is incremental search that related to the sign change. Sometimes, this technique is called binary chopping, or Bolzano's method.The False-Position Method: It's the improved tech…

There are several methods available to solve the root finding problem such as "bracketing methods" and "Open methods".

The bracketing methods require 2 initial guesses for the root. These guesses must "bracket" the root. The numerical methods using bracketing methods consist of the following techniques:

The Bisection Method: The idea of this technique is incremental search that related to the sign change. Sometimes, this technique is called binary chopping, or Bolzano's method.The False-Position Method: It's the improved tech…