JUST NEED THE MATHEMATICAL PART. THANKS!!! Write a C++ program to solve the foll

Question

JUST NEED THE MATHEMATICAL PART.

THANKS!!!

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

program for non-lier equation

#include <stdio.h>

#include <math.h>

#include <iostream.h>

void main()

{

double a,b,c,d,detj,detjinv,jinv11,jinv12,jinv21,jinv22,F1,F2,deltax,deltay;

double x,xi,y,yi;

int counter = 0;

cout << " Enter the initial value for T1: ";

cin >> xi;

cout<<" Enter the initial value for T2: ";

cin>>yi;

double f = 0.1;

x = xi;

//y = yi;

int check = 0 ;

while (check ==0)

{

F1 = -322.325*x+1.243*pow(10,-9)*(pow(x,4))-0.6579*y-1.243*pow(10,-9)*(pow(y,4))-52321.635;

F2 = 340.4886*x-9.1821*y-55478.8706+2.379*pow(10,-17)*pow((322.9827*x+169.5321*y-52321.635),4);

a = -322.325+4.972E-9*(pow(x,3));

b = -0.6579-4.972E-9*(pow(x,3));

c = 17.4932+(3.074*pow(10,-14))*pow((52321.635+322.9829*x+169.5321*y),3)-322.9829;

d = 9.1821+(9.5176*pow(10,-17))*pow((52321.635+322.9829*x+169.5321*y),3);

detj = a*d - b*c;

jinv11 = d/detj;

jinv12 = -b/detj;

jinv21 = -c/detj;

jinv22 = a/detj;

detjinv = (((a*d)/(detj*detj)) - ((b*c)/(detj*detj)));

deltax = (jinv11*F1*f)+(jinv12*F2*f);

deltay = (jinv21*F1*f)+(jinv22*F2*f);

x = x-deltax;

y = y-deltay;

}

if((F1 < 0.001) && (F2 < 0.001)

{ check = 1;

}

cout<<" F1 = "<<F1;

cout<<" F2 = "<<F2;

cout<<" x = "<<x;

cout<<" y = "<<y;

}

Program for Newton–Raphson method for computing the approximate of the square root.

program for linear latest squares

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