DOC: Add example in README

README.md

@@ -2,4 +2,52 @@
 
 [![Build Status](https://travis-ci.org/davidkleiven/gononlin.svg?branch=master)](https://travis-ci.org/davidkleiven/gononlin)
 
-Package for solving non-linear systems of equations. 
+Package for solving non-linear systems of equations. The package implements Jacobian-Free Newton
+Krylov method, where the Jacobian is approximated via finite differences. However, since the Krylov space methods only require the action of the Jacboian on a search direction *v*, the full
+Jacobian matrix is never explicitly stored, which makes the technique very memory efficient.
+
+# Example
+
+```go
+import (
+	"fmt"
+	"math"
+
+	"github.com/davidkleiven/gononlin/nonlin"
+)
+
+func ExampleNewtonBCGS() {
+	// This example shows how one can use NewtonBCGS to solve the
+	// system of equations
+	// (x-1)^2*(x - y) = 0
+	// (x-2)^3*cos(2*x/y) = 0
+
+	problem := nonlin.Problem{
+		F: func(out, x []float64) {
+			out[0] = math.Pow(x[0]-1.0, 2.0) * (x[0] - x[1])
+			out[1] = math.Pow(x[1]-2.0, 3.0) * math.Cos(2.0*x[0]/x[1])
+		},
+	}
+
+	solver := nonlin.NewtonBCGS{
+		// Maximum number of Newton iterations
+		Maxiter: 1000,
+
+		// Stepsize used to appriximate jacobian with finite differences
+		StepSize: 1e-2,
+
+		// Tolerance for the solution
+		Tol: 1e-7,
+	}
+
+	x0 := []float64{0.0, 3.0}
+	res := solver.Solve(problem, x0)
+	fmt.Printf("Root: (x, y) = (%.2f, %.2f)\n", res.X[0], res.X[1])
+	fmt.Printf("Function value: (%.2f, %.2f)\n", res.F[0], res.F[1])
+
+	// Output:
+	//
+	// Root: (x, y) = (1.00, 2.00)
+	// Function value: (-0.00, 0.00)
+}
+```

nonlin/nonlin_example_test.go

@@ -11,7 +11,7 @@ func ExampleNewtonBCGS() {
 	// This example shows how one can use NewtonBCGS to solve the
 	// system of equations
 	// (x-1)^2*(x - y) = 0
-	// (x-2)^2*cos(2*x/y) = 0
+	// (x-2)^3*cos(2*x/y) = 0
 
 	problem := nonlin.Problem{
 		F: func(out, x []float64) {