Nonlinear Equations Solution
| Variable | Value | f(x) | Initial Guess | Initial f(x) | |
|---|---|---|---|---|---|
| 1 | a | 1.0001094 | -8.9e-16 | 2 | 7.0e+0 |
| 2 | c | 3.0006565 | 9.5e-15 | 2 | -5.9e-1 |
| 3 | b | 2.0005471 | 7 | ||
| 4 | d | 3.9996717 | -13 | ||
| 5 | e | 4.9996385 | -9.914 |
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 | 5 | Setting |
| 2 | Implicit equations | 2 | Setting |
| 3 | Explicit equations | 3 | 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) c, a |
| 2 | ℹ️ Info | Explicit variables (3) b, d, e |
| 3 | ℹ️ Info | All variables (5) c, a, b, d, e |
| 4 | ℹ️ Info | Solved using the primary nonlinear equations solver Method 1 (Safe-Newton); 4 iterations in this attempt. |
Source
# Simultaneous equations solver
# Verified Solution: a=1.00011, b=2.00055, c=3.00066, d=3.99967, e=4.99964
f(c) = 3.8907-ln(6*c)-a
f(a) = a+b-c
b = 5*a-3
d = 2*c+4-3*b
e = sin(d*7.5*3.1416/180)/0.1
c(0) = 2
a(0) = 2
# Verified Solution: a=1.00011, b=2.00055, c=3.00066, d=3.99967, e=4.99964
f(c) = 3.8907-ln(6*c)-a
f(a) = a+b-c
b = 5*a-3
d = 2*c+4-3*b
e = sin(d*7.5*3.1416/180)/0.1
c(0) = 2
a(0) = 2