Taylor (Lab 1)

#include <stdio.h>                                                      // Thanasis Tsounakis 2021 NEWTON-RAPHSON METHOD
#include <stdlib.h>
#include <math.h>

double f(double x){                                                     // f(x) function
    return x + exp(-10 * pow(x,2)) * cos(x);
}

double df(double x){                                                    // f'(x) derivative function of f(x)
    return 1.0 - exp(-10 * pow(x,2)) * ( sin(x) + 20 * x  * cos(x));
}

double ddf(double x){                                                   // f''(x) derivative function of f(x)
    return exp(-10 * pow(x,2)) * (400 * pow(x,2) * cos(x) + 40 * x * sin(x) - 21 * cos(x));
}

int main(){
    double x, x0 = -0.7;                                                // variable x and initial value of x (x_0)
    double error;
    int k = -10, i = 0;

    printf("i:\tx:\t\tf(x):\t\tError:\n");

    do{
        i++;
        x = x0 - 2 * (f(x0) * df(x0) / (2*pow(df(x0),2) - f(x0)*ddf(x0)));
        error = fabs(x - x0);
        printf("%3d\t%14.10f\t%14.10f\t%14.10f\n", i, x, f(x), error);  // print the data of the calculations
        x0 = x;
    } while(error >= 0.5 * pow(10.0,k));                                // do until error is smaller than 10^-10

    getchar();
    return 0;
}