Write a C++ program to solve the following system of three non-linear equations

Question

Write a C++ program to solve the following system of three non-linear equations in three variables, using the Method of Newton-Raphson: x^3 + 3y = 1/sin^2(2 theta) y = e^-x y = x + ln(theta) Start the iterations with the following initial guesses: {1,1,1}^T Evaluate the partial derivatives required by the Jacobian Matrix using a centered finite difference approximation Solve for the errors of each variable using simple Gaussian Elimination Proceed with the iterations until the following equation is satisfied: sigma all variables abs(epsilon) LE 10^-5 Your program must display the Jacobian matyrix and the "current" value of each of the variables at every iteration.

Explanation / Answer

Hi..

Following is the snippet for Newton-Raphson method. You can use the same to enter your three equations (or n equations) . This would then provide with accurate results.

int main()
{
char initial = 'c';
double E;
int i=0,s=1,r=1;
double N = 12;
double a,b,c,d;
double fx,fpx,y,y;

while(initial == 'q')
{
  printf("Enter the values of a, b, c and d");
cin>>a;
cin>>b;
cin>>c;
cin>>d;
  if(a == 0)
   break; // exit

  cout<<"Enter the value of y ";
  cin>>y;

  cout<<"Enter the value of E: ";
  cin>>E;

  y= y;
  fx = a*y*y*y +b*y*y +c*y +d;
  i=0;

  while(i<N)
  {
   i=i+1;

   fx = a*y*y*y +b*y*y +c*y +d;
   fpx = 3*a*y*y +2*b*y +c;
   y= y - (fx/fpx);

   cout<<"Values"<< r1<< y;
  }

  cin>>initial;

  cout<<"'q' to quit: ";

  cin>>initial;
}

return 0;
}

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