Nonlinear Equations Solution
| Variable | Value | f(x) | Initial Guess | Initial f(x) | |
|---|---|---|---|---|---|
| 1 | x | 5 | -2.8e-12 | 2 | 2.1e+2 |
| 2 | y | 20 | 1.3e-12 | 10 | -8.4e+1 |
Iteration Progress
log10(maxᵢ|fᵢ(x)|) measures the largest absolute equation residual per iteration.
Lower values indicate a better solution.
For example, -7 means every equation residual is at most approximately 10⁻⁷.
The red line shows the configured function-residual tolerance.
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Number of equations | 2 | Setting |
| 2 | Implicit equations | 2 | Setting |
| 3 | Explicit equations | 0 | Setting |
| 4 | Elapsed time | 0.00 sec | Setting |
| 5 | Solution method | safenewt | Setting |
| 6 | Max iterations | 150 | Setting |
| 7 | Tolerance F | 1e-7 | Setting |
| 8 | Tolerance X | 1e-7 | Setting |
| 9 | Tolerance min | 1e-7 | Setting |
| 10 | #@report_fix_digits = 8 | Default (integer) | |
| 11 | #@report_show_source = true | Default (boolean) | |
| 12 | #@report_show_header = false | Default (boolean) | |
| 13 | #@report_show_settings = true | Default (boolean) | |
| 14 | #@report_show_charts = true | Default (boolean) | |
| 15 | #@chart_size = 428,300 | Default (array) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | ℹ️ Info | Implicit variables (2) x, y |
| 2 | ℹ️ Info | All variables (2) x, y |
| 3 | ℹ️ Info | Solved using the primary nonlinear equations solver Method 1 (Safe-Newton); 5 iterations in this attempt. |
Source
# NLE System: Solve 2 nonlinear equations:
# 2*x + x*y - y^2 = -290
# x*log(y/2) + x*y = 105
# Verified Solution: x=5, y=20
f(x) = 2*x + x*y - y^2 + 290
f(y) = x*log(y/2) + x*y - 105
x(0) = 2
y(0) = 10
# 2*x + x*y - y^2 = -290
# x*log(y/2) + x*y = 105
# Verified Solution: x=5, y=20
f(x) = 2*x + x*y - y^2 + 290
f(y) = x*log(y/2) + x*y - 105
x(0) = 2
y(0) = 10