Solve Nonlinear Equations Online

Nonlinear equations occur in all fields of engineering. A given task is reduced to the form f(x)=0. The object is to find values of x that satisfy this condition. This doesn't always have to be ALL values. Most times, we are interested only in values between xmin and xmax.

Often it is difficult, if not impossible, to find an explicit solution. With the aid of computer power, the approximate solutions made possible by numerical analysis are readily attainable. The ancient method of halving the interval, whose inefficiency when done by hand has spawned numerous more efficient methods, can be safely resurrected.

The method requires a graph of f(x) to be drawn between xmin and xmax. Where the graph crosses the 0-line, we have a solution. This online service of Engineers Compendium was inspired by the clever work of Lutz Tautenhahn, who developed the JavaScript Diagram Builder.

How do you use this service?

Your biggest challenge is to express your task in the form f(x)=0, where f(x) must be written in Javascript math syntax. Javascript is very good at many things, but mathematics isn't one of them. You have four operators plus brackets, eight built-in constants, and seventeen functions at your disposal.

The operators are: + - * / (not even ^, but there is pow)
The constants are: E LN2 LN10 LOG2E LOG10E PI SQRT1_2 SQRT2
The functions are: abs acos asin atan ceil cos exp floor log max min pow random round sin sqrt tan

It is amazing what creative minds can do with this meagre fare. Check out some of the examples in the margin. You are encouraged to submit your own solution to this growing list. Your rewards for doing so are:

• Free use of the service.
• Peer review of your logic.
• Recognition and kudos.
• Personal satisfaction.

When you have your f(x), type it into the formula box. You know the range of xmin and xmax where results are of interest to you. You also know the approximate ymin and ymax to be expected within this range. This isn't important to the solution, but it produces a nice graph. Type these values into the appropriate boxes. Note that ymin must be less than 0 and ymax must be greater than 0. Logically, if the graph doesn't straddle the 0-line, there is no solution within the range of interest.

Finally, decide your error-tolerance, type this into the box labelled "Tol:", and click <Solve>. There are three things to know about the tolerance:

1. The value must be a positive decimal fraction.
2. The number of zeros after the decimal point controls the number of digits that will be displayed in the result (up to five).
3. If you enter more than five zeros after the decimal point, all 15 digits of Javascript math will be displayed.

go to top

.