## Multi-dimensional Root-finder - Two Nonlinear Equations in Two Unknowns |

This page contains a utility that attempts to compute the roots of a system of two nonlinear equations in two unknowns.

**References:**

The utility posted on this page is a JavaScript translation of the FORTRAN routine SNSQE, by K. L. Hiebert (SNLA), which is posted on the SLATEC site as SNSQE.

Although all care has been taken to ensure that the sub-routines were translated accurately, some errors may have crept into the translation. These errors are mine; the original FORTRAN routines have been thoroughly tested and work properly. Please report any errors to the webmaster.

The program posted on this page attempts to compute the roots of a system of two nonlinear equations in two unknowns:

f_{1} = 0

f_{2} = 0

where the a_{ij} and c_{i} are constant coefficients.

Values for *all* of these coefficients may not be necessary--in which case, make sure there is a "0" in the unused fields--but, by providing many fields, the intention is to make this program applicable to a wider range of problems.

**HOW TO USE THIS UTILITY**

Enter the appropriate values for the coefficients in the data fields below.

Also enter an initial estimate for the solution vector **x**_{o} = (x_{o}, y_{o})^{T}.

(Note that numbers in scientific notation are NOT recognized)

Once you click the "Seek Solution" button, this utility will seek a solution vector **x** = (x, y)^{T} that solves the system . This vector, and the values of f_{1} and f_{2} at that point, are output below.

**IMPORTANT!** Note the error code.

There are systems for which solutions cannot be found. In these cases, the program terminates after a specific number of iterations; values for the latest iterate are output, but they are not necessarily a solution.

For more information about this program, please see the associated blog post: Multi-dimensional Root-finder - Two Nonlinear Equations in Two Unknowns