Mechanical Design Handbook

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In the previous post , we talked about several root finding techniques. In this post, we're going to see how we can use Microsoft Excel VBA to find the roots using Newton-Raphson Method. As we know that Newton-Raphson Method is the most widely used of all root-locating formulas. The Newton-Raphson method uses the slope ( first derivative ) of the function to find the root. That means, in the VBA code, we have to find the first derivative of the function in order to find the root. We already have the VBA code to find the first derivative and we're going to use it again in Newton-Raphson Method. The Newton-Raphson Method uses 2 terms of taylor series to approximate delta x as shown below. f(x) = f(x 0 ) + (x N - x 0 )f'(x 0 ) = 0 (x N - x 0 )f'(x 0 ) = -f(x 0 ) x N - x 0 = -f(x 0 )/f'(x 0 ) delta x = -f(x 0 )/f'(x 0 ) The followings are the procedure to find the root using Newton-Raphson Method. Guess the initial value of the root --> sele

In the previous post, Numerical Methods - First derivative using Excel formula , we know how to calculate the first derivative of functions using formula in Microsoft Excel. In this post, let's see how we can simplify it by using Excel VBA code. The VBA is just like this. ' ================================================ ' Created by Suparerg Suksai ' Mechanical Design Handbook ' http://mechanical-design-handbook.blogspot.com ' ' First Derivative - Numerical Methods ' ================================================ Function f(x As Double ) As Double   f = 5 * (x - 3) ^ 3 - 4 * x ^ 2 - Sin(2 * x) End Function Function fDeriv(x As Double ) As Double Const h = 0.00001 ' Step size fDeriv = (-f(x + 2 * h) + 8 * f(x + h) - 8 * f(x - h) + f(x - 2 * h)) / 12 / h End Function The highlighted (yellow) text is the function that we want to calculate for the first derivative. We can simply replace it with new function. The remaining c