Question

write a c code for df/dx=x^2 solution with a boundary condition f(1)= 2 and h= 0.01

Answer 1

//We are going to use Euler's method of solving differential equation
//Here, y_next = y_prev + h*function(x_prev, y_prev)
//we have f(x) = x^2

#include<stdio.h>
double function(double);
int main() {
        int i = 0;
        double x_prev, x_next;
        double y_next, y_prev, h;
        h = 0.01;                                       //step size
        x_prev = 1;                                     //initial value of x
        y_prev = 2;                                     //boundary value
        do {
                y_next = y_prev + h * function(x_prev);
                x_next = x_prev + h;
                printf("x\t\ty\t\th\n");
                printf("%4.6lf\t%4.6lf\t%4.6lf\n", x_next, y_next, h);
                x_prev = x_next;
                y_prev = y_next; 
                i++;
        } while (i<20);                      //You can also use y_next-y_prev <0.001 like condition
        getchar();
        return 0;
}
double function(double x) {
        return x*x;
}