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

# Example 9 - NLE System
# Simultaneous linear and nonlinear equations
# 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


Calculated values

    Variable Value f(x) Initial Guess Initial f(x)
1 a 1.0001094 -8.9E-16 2 7.0E00
2 c 3.0006565 9.5E-15 2 -5.9E-01

    Variable Value Initial Value
1 b 2.0005471 7
2 d 3.9996717 -13
3 e 4.9996385 -9.9144434

Formatted equations

  f c ( ) = 3 . 8 9 0 7 l n 6 c ( ) a = 0
  f a ( ) = + a b c = 0
  b = 5 a 3
  d = + 2 c 4 3 b
  e = s i n d 7 . 5 3 . 1 4 1 6 1 8 0 0 . 1

Nonlinear equations

1 f(c) = 3.8907-ln(6*c)-a = 0
2 f(a) = a+b-c = 0

Explicit equations

1 b = 5*a-3
2 d = 2*c+4-3*b
3 e = sin(d*7.5*3.1416/180)/0.1

General Settings

Total number of equations 5
Number of implicit equations 2
Number of explicit equations 3
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