Zero Find

To find zeros of the currently defined function select this command from the Mode Menu. The Zero Finding window will be displayed.

You may select from three methods to use for finding zeros of the function

• Newton-Raphson
  
• Bisection
  
• User-defined function

The Newton-Raphson method is explained in Chapter 12 of Mathematics for Electrical Engineering and Computing.

Bisection Method

The Bisection method works by iteratively considering an interval [a,b], at the end points of which the function has opposite sign. The interval is bisected and, as long as the function is locally continuous, one of the two new intervals must still satisfy the original condition that at the end points the function has opposite sign. This process continues until the interval is so small that the mid-point of the interval is considered to be the position of the zero of the function. The advantage of the bisection method is that it will always give a result, if a suitable starting interval can be found. It can, however, be very slow.

User Defined Zero Find

The user-defined method depends on applying a suitable fix-point function. You input the fix-point function that you wish to use by pressing the Function Button on this window. The method for defining this function is identical to that used to define the General Function

A fix-point function is found by rearranging the equation y(t)=0 into the form t=fix(t). Some of the Problems given in this help text suggest some suitable fix-point functions to use.

You can also change the settings for the desired accuracy of the solution and the number of iterations to use on this window.

When you are satisfied with the settings for zero finding select OK. plotXpose is now in zero finding mode. When you click or touch near the t-axis (two points are required for the Bisection method) plotXpose will attempt to find a zero of the function using the method you have defined. To take it out of zero finding mode select the Clear Mode command.

When a zero has been found to the required accuracy, or the number of iterations has been surpassed, a popup with the solution to y(t)=0 or a warning that the method failed to converge will be displayed.

A message box will report a summary of the process. The summary consists of the sequence of values (n, t, y(t)). If zero finding has been successful y(t) should be very small, i.e. approximately 0.

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