Chapter 7: Collection and Analysis of Rate Data

Polymath Non-Linear Equation Solver Tutorial


This tutorial will explain the use of Polymath's non-linear equation solver.

First, launch Polymath. You should see a menu bar at the top of the scren that looks like this.

Screenshot of the POLYMATH 6.10 Educational Release window, showing the menu bar with options for File, Program, Window, and Help. Several icons are visible, including options for opening files, saving, cutting, copying, and accessing various mathematical functions and settings.

Click on the NLE button (function button) to bring up the menu for the non-linear equation solver. The menu should look like this.

Screenshot of the POLYMATH 6.10 Educational Release window, showing the menu bar with options for File, Program, Edit, Format, Problem, and Help. The interface shows fields for entering equations with a label 'Nonlinear Equations Solver', along with controls for defining functions, an empty equation input field, and a status message indicating 'No equations entered'.

From here we need to enter our non-linear equations, so click on the " f(x)+ " button. You should see a screen that looks like this.

Screenshot of the Nonlinear Equations Solver interface, showing fields to enter a nonlinear equation and its initial guess. The equation is in the format f(A) = A + B^2, with an input field for the initial guess A(0) = 1. The options at the bottom include 'Clear', 'Done', and 'Cancel'.

Note that the no matter what variable you enter in the "f( )" box, the equation that you input will be solved to find when it equals 0. Make sure that the variable you do enter into the "f( )" box is one of the variables that you want Polymath to vary in searching for a solution to the NLE. Enter an initial guess for the variable and click done to go back and add more equations. When you are done entering equations, the screen should look like this.

Screenshot of the POLYMATH 6.10 Educational Release window showing nonlinear equations for A and B. The equations displayed are f(B) = 2*B - A^2 - 3 and f(A) = A + B^2 with initial guesses for both A and B set to 1. The interface is marked as 'Ready for solution' with options for solving the equations.

When you are ready to run the solver, just click the pink Solve arrow. You should get a report window that looks like this.

Screenshot of POLYMATH 6.10 Educational Release showing the solution for nonlinear equations. The table displays the calculated values for variables A and B, their corresponding f(x) values, and initial guesses. The equations f(B) = 2*B - A^2 - 3 and f(A) = A + B^2 are listed. General settings for the solution method (SAFENWT), iterations, and tolerance values are also shown.

If the window says something about the solver not converging, one of two things is happening. Either your guesses for the variables are too far off from their true values, which means you need to enter better guesses, or the system you have entered is insolvable, so you should check your equations for errors.

This is basically all you need to get started using Polymath to solve NLEs.

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