Category: Numerical Methods

Suppose that in a spreadsheet the following formula is entered into cell B1: Since cell reference B1 is in the formula of the same cell, this is called a “circular reference.” Normally, Excel will complain about this. However, if the Enable Iterative Calculations (see File/Options/Formulas) box is checked, Excel will immediately do the following: 1. It will automatically use an initial…

If it is (somehow) known that a root lies in the interval [a, b], then by simply halving the interval in which the root lies, the interval can be reduced to an acceptable level. This idea is at the heart of the bisection method as shown in Figure 1.2. The restriction is that f(a) and f(b) must have opposite signs—one…

Excel has very good plotting capabilities. Unfortunately, it is not possible in Excel to simply give a command such as plot(f(x)). It is necessary to produce a list or table of x and f(x) values and to graph the resulting data. This is best illustrated by an example. Example 1.1: Plotting the Equation A table of data and…

In Chapter 4, methods for approximating the derivative of a function using finite differences are presented. The secant method uses the idea of finite differences to approximate the derivative in the Newton method formula. Starting with two initial guesses x0 and x1, which need not bracket the root of interest, the approximation to f΄(x) can be written as follows: Or, in general, after k steps or iterations,…

Many engineering problems require the solution of a single nonlinear equation. Such an equation can always be cast into the form The objective of this chapter is to study methods and learn of Excel® tools for finding the root(s) of a nonlinear equation, that is, for finding x such that f(x) = 0. Simple algebra provides the root for…