Non-Linear Equation Root Finder

Many engineering math problems result in a need to solve non-linear equations. Solving these equations can be complex, tedious and in some situations, no solution may exist at all. The Non-Linear Equation Root Finder is a utility that allows you to quickly solve for the root of any user-defined non-linear equation. This helps you eliminate some of the guesswork of solving for the value of the unknown variable that brings the function as close to zero as possible.

You can access the utility by choosing Home > Tools > Non-Linear Equation Root Finder.

The following is an example of a calculation for the root of an equation.

To use the utility, follow the steps below:

Enter the user-defined equation in the Function field. Use the variable x for the unknown variable.
In the Root Minimum and Root Maximum fields, enter the initial guess estimates of the root.
In the Algorithm Order field, enter the variable order which is to be improved in every iteration. Note that the algorithm order must be greater than or equal to 2.
In the Convergence field, set a tolerance value at which the root of the equation should converge (i.e., f(x) = 0).
In the Max Iterations field, set the maximum number of iterations the algorithm will perform in order to solve for the root of the equation.

Click Calculate to solve for the root of the equation. You may need to edit the inputs in order to obtain the best possible solution for the equation. The Results area will return the following:

Real Root returns the root of the equation. If the root is not within the initial specified range, you will need to edit the values in the Root Minimum and Root Maximum fields until the root is within range of those values.
Function Value shows the value of the user-defined equation at the root value. You may need to edit the tolerance value in the Convergence field in order to obtain a solution that is as close as possible to zero.
Iterations returns the number of iterations that were performed in order to obtain the solution.