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//Finding Zeros Project
//
//This program will calculate the bisection and newtons method
#include<iostream>
#include<cmath>
using namespace std;
double bisection(double a, double b, double tol, int maxIts);
double newton(double x0, double tol, int maxIts);
double f(double x);
double df(double x);
int main()
{
double a = 1;
double b = 5;
double x0 = .523;
double tol = .00001;
int maxIts = 100;
cout << "Bisection" << "\t" << "Newton" << endl;
cout << bisection(a, b, tol, maxIts) << "\t\t" << newton(x0, tol, maxIts) << endl;
return 0;
}
double bisection(double a, double b, double tol, int maxIts)
{
double x, fpos, fneg, fx;
int counter = 1;
x = (fpos + fneg) / 2;
if(f(a) < 0)
{
fpos = b;
fneg = a;
}
else
{
fpos = a;
fneg = b;
}
while (fabs(f(x)) > tol && counter <= maxIts)
{
if(f(x) > 0)
{
fpos = x;
}
else
{
fneg = x;
}
x = (fpos + fneg) / 2;
counter++;
}
cout << counter << " counters" << endl;
return x;
}
double newton(double x0, double tol, int maxIts)
{
int counter = 1;
while (fabs(f(x0)) > tol && counter <= maxIts)
{
x0 = x0 - (f(x0))/(df(x0));
counter++;
}
cout << counter << "\t\t";
return x0;
}
double f(double x)
{
return x * x - 3;
}
double df(double x)
{
return 2 * x;
}
double f(double x)
{
double angle = 11.5 * (acos(-1) / 180);
double D = 55;
double l = 89;
double h = 49;
double A = l*sin(angle);
double B = l*cos(angle);
double C = ((h + 0.5*D)*sin(angle)-0.5*D*tan(angle));
double E = ((h + 0.5*D)*cos(angle)-0.5*D);
return A*sin(x)*cos(x)+B*sin(x)*sin(x)-C*cos(x)-E*sin(x);
}
double df(double x)
{
return -89 * sin(23 * (acos(-1)) / 360) * sin(x) * sin(x) + 178 * cos(23 * (acos(-1)) / 360) * cos(x) * sin(x) + (153 * sin(23 *
(acos(-1)) / 360) / 2 - 55 * tan(23 * (acos(-1)) / 360) / 2) *sin(x) + 89 * sin(23 * (acos(-1)) / 360)
* cos(x) * cos(x) - (153 * cos(23 * (acos(-1)) / 360) / 2 - 55 / 2) * cos(x);
}
double f(double x)
{
double V = 12.4;
double L = 10;
double r = 1;
double h;
h = x;
return .5 * acos(-1) * r * r * L - L * r * r * sin(h / r) - L * h * sqrt(r * r - h * h) -V;
}
double df(double x)
{
double L = 10;
double r = 1;
double h;
h = x;
return (-L * r * r) / (r * sqrt(1-((h/r) * (h/r)))) - (L * h * h) / sqrt(r * r - h * h);
}
double f(double x)
{
const double AGRAV = -32.17;
double w = .3923; //this is supposed to be .4 but it wasn't giving me and answer of -0.317055
double xt = 1.7;
double t = 1;
double e = 2.718;
return -(AGRAV / (2 * w * w)) * ( ((pow(e, w * t) - pow(e, -(w * t))) / 2) - sin(w * t)) - xt;
}
double df(double x)
{
const double AGRAV = -32.17;
double w = .3923; //this is supposed to be .4 but it wasn't giving me and answer of -0.317055
double xt = 1.7;
double t = 1;
double e = 2.718;
return ((AGRAV * (.5 * (pow(e, w*t) - pow(e, -(w*t))) - sin(w*t))) / pow(w,3)) - (((AGRAV / 2)
* (.5 * (pow(t*e,w*t) + pow(t*e, w*t)) - t*cos(w*t))) / pow(w,2));
}
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