The Newton-Raphson method is a powerful numerical technique used to find the roots of a real-valued function. It is a popular method for solving equations that cannot be solved analytically, and it has numerous applications in various fields, including engineering, physics, and finance. In this article, we will explore how to code the Newton-Raphson method in Excel VBA, a powerful tool for numerical computations.
Mathematically, the Newton-Raphson method can be expressed as:
The Newton-Raphson method is an iterative method that uses an initial guess for the root of a function to converge to the actual root. The method is based on the idea of approximating the function at the current estimate of the root using a tangent line. The slope of the tangent line is given by the derivative of the function at the current estimate. The next estimate of the root is then obtained by finding the x-intercept of the tangent line.
where \(x_n\) is the current estimate of the root, \(f(x_n)\) is the value of the function at \(x_n\) , and \(f'(x_n)\) is the derivative of the function at \(x_n\) .
\[x_{n+1} = x_n - rac{f(x_n)}{f'(x_n)}\]