PolymathPlus Report
📈   Nonlinear Equations 2022-04-01 12:33 

# Example 8 - NLE System
# Solve a system of 2 nonlinear equations:
# [1] 2*x + x*y - y^2 = -290
# [2] 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


Calculated values

    Variable Value f(x) Initial Guess Initial f(x)
1 x 5 -2.5E-12 2 2.1E02
2 y 20 1.3E-12 10 -8.4E01

Formatted equations

  f x ( ) = + + 2 x x y y 2 2 9 0 = 0
  f y ( ) = + x l o g y 2 x y 1 0 5 = 0

Nonlinear equations

1 f(x) = 2*x + x*y - y^2 + 290 = 0
2 f(y) = x*log(y/2) + x*y - 105 = 0

General Settings

Total number of equations 2
Number of implicit equations 2
Number of explicit equations 0
Elapsed time 0.00 sec
Reporting digits 10
Solution method safenewt
Max iterations 150
Tolerance F 1E-07
Tolerance X 1E-07
Tolerance min 1E-07