The equations of a circle and a sine curve are graphed above. These two equations are coupled and nonlinear in x and y. Coupled nonlinear algebraic equations frequently arise in the determination of the static equilibrium configuration of a mechanical system.

The Autolev file nonlinearSolve.al is a complete listing of the Autolev commands to:

• produce a C code for exceptionally fast numerical solution of this coupled set of nonlinear algebraic equations
• produce a nicely-formatted C input file nonlinearSolve.in that allows one to input starting "guess" values for x and y that converge to the solution in its neighborhood (as is obvious from the figure above, there are two solutions to this set of equations)

After compiling and running the C program, the PC executable nonlinearSolve.exe produces the output file nonlinearSolve.1 which is a record of the input guess for x and y, the output (converged) result for x and y, and a measure of the closeness to zero that was achieved. As is clear, the output values x=0.73908513 and y=0.67361203 are highly accurate solutions to the nonlinear algebraic equations.