Let us take the initial guesses of the root of as and. Figure 3 Graph of the function f(x).Įxample 1 Cont. Figure 2 A loaded bookshelf.Įxample 1 Cont. Find the absolute relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration. Conduct three iterations to estimate the root of the above equation. The equation that gives the position x where the deflection is maximum is given by Use the secant method of finding roots of equations to find the position where the deflection is maximum. Hence to find the maximum deflection we need to find where and conduct the second derivative test.Įxample 1 Cont. The vertical deflection of the shelf is given by where x is the position where the deflection is maximum. You want to find the maximum vertical deflection of the bookshelf. The material is wood having Young’s Modulus 3.667 Msi, thickness 3/8 ” and width 12”. Įxample 1 You are making a bookshelf to carry books that range from 8 ½ ” to 11” in height and would take 29”of space along length. Also check if the number of iterations has exceeded the maximum number of iterations. If so, go back to step 1, else stop the algorithm.
![usf download matlab 2014a free usf download matlab 2014a free](https://cyberleninka.org/viewer_images/335489/f/1.png)
Step 2 Find if the absolute relative approximate error is greater than the prespecified relative error tolerance.
![usf download matlab 2014a free usf download matlab 2014a free](https://cyberleninka.org/viewer_images/902204/f/1.png)
Step 1 Calculate the next estimate of the root from two initial guesses Find the absolute relative approximate error The secant method can also be derived from geometry: can be written as On rearranging, the secant method is given as Secant Method – Derivation The Geometric Similar Triangles Figure 2 Geometrical representation of the Secant method. Secant Method – Derivation Newton’s Method Approximate the derivative Substituting Equation (2) into Equation (1) gives the Secant method (1) (2) Figure 1 Geometrical illustration of the Newton-Raphson method. Secant Method Civil Engineering Majors Authors: Autar Kaw, Jai Paul Transforming Numerical Methods Education for STEM Undergraduates 07/28/10