POLYMATH Report          NLE 
 Nonlinear Equations 2016-May-30 

Calculated values of NLE variables
    Variable Value f(x) Initial Guess Initial f(x)
1 a 1.00011 -8.9E-16 2 7.0E00
2 c 3.00066 9.5E-15 2 -5.9E-01

    Variable Value Initial Value
1 b 2.00055 7
2 d 3.99967 -13
3 e 4.99964 -9.91444

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

Problem source text
# S. 9 - NLE System
# Simultaneous linear and nonlinear equations
# Verified Solution: a = 1.00011, b = 2.00055
# c= 3.00066,d = 3.99967 and e = 4.99964.
f(c)=3.8907-ln(6*c)-a
c(0)=2
f(a)=a+b-c
a(0) = 2
b=5*a-3
d=2*c+4-3*b
e=sin(d*7.5*3.1416/180)/0.1

Matlab formatted problem
Create m file called PolyNles.m and paste the following text into it.
% S. 9 - NLE System
% Simultaneous linear and nonlinear equations
% Verified Solution: a = 1.00011, b = 2.00055
% c= 3.00066,d = 3.99967 and e = 4.99964.
function PolyNles
   xguess = [2 2]; % initial guess vector
   x = fsolve(@MNLEfun, xguess);
   fprintf('The NLEs solution is:\n');
   fprintf('c = %g\n',x(1));
   fprintf('a = %g\n',x(2));
end

function fvec = MNLEfun(IndepVarsVec)
   c = IndepVarsVec(1);
   a = IndepVarsVec(2);
   b = 5 * a - 3;
   d = 2 * c + 4 - (3 * b);
   e = sin(d * 7.5 * 3.1416 / 180) / 0.1;
   fvec(1,1) = 3.8907 - log(6 * c) - a;
   fvec(2,1) = a + b - c;
end

General Settings
Total number of equations 5
Number of implicit equations 2
Number of explicit equations 3
Elapsed time 0.00 sec
Reporting digits 8
Solution method safenewt
Max iterations 150
Tolerance F 1E-07
Tolerance X 1E-07
Tolerance min 1E-07