Euler's Method (iterative).

euler.c

/**
Euler's Method (iterative).
@author Tyler Weaver

Compile:
gcc euler.c -o euler
Run:
./euler
*/

#include <stdio.h>
#include <stdbool.h>

#define X 	0
#define Y 	1

double function(double x, double y);
void euler(double step_size, double target_x, 
	double initial_x, double initial_y,
	double (*func)(double,double), bool debug);

int main()
{
	const double step_size = 0.1;
	const double initial_value[2] = {0,1};
	const double target_x = 0.5;
	
	euler(step_size, target_x, initial_value[X], initial_value[Y],
		function, true);

	return 0;
}

double function(double x, double y)
{
	long double value = x*y + y;
	return value;
}

void euler(double step_size, double target_x, 
	double initial_x, double initial_y,
	double (*func)(double,double), bool debug)
{
	const int n_steps = (target_x / step_size);

	double prev_value[2] = {initial_x, initial_y};
	double value[2];

	if(debug)
	{
		printf("Step Size: %f\r\n", step_size);
		printf("Initial value: (%f,%f)\r\n", initial_x, initial_y);
		printf("Target x value: %f\r\n", target_x);
		printf("Number of steps: %d\r\n", n_steps);
	}

	for(int i = 0; i < n_steps; i++)
	{
		value[X] = prev_value[X] + step_size;
		value[Y] = prev_value[Y] + (step_size*func(prev_value[X], prev_value[Y]));

		if(debug)
		{
			printf("\r\nfunc(x,y) = %f\r\n", func(prev_value[X], prev_value[Y]));
			printf("value[y] = %f + %f * %f = %f\r\n", prev_value[Y], 
			 	step_size, func(prev_value[X], prev_value[Y]), value[Y]);
		}
		printf("(%f,%f)\r\n", value[X], value[Y]);
		prev_value[X] = value[X];
		prev_value[Y] = value[Y];
	}
}