Euler's Method (recursive).

euler_r.c

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

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

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

#define X 	0
#define Y 	1

double function(double x, double y);
double 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;
	double output;
	
	output = euler(step_size, target_x, initial_value[X], initial_value[Y],
		function, true);

	printf("output = %f\r\n", output);

	return 0;
}

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

double euler(double step_size, 
	double target_x, double x, double y,
	double (*func)(double,double), bool debug)
{
	double target_y; // the output value we are looking for

	if(x == target_x) // we have reached the end
		return y;
	else
	{
		y = y + (step_size*func(x, y)); // calculate the new y value
		x = x + step_size;				// update x
		if(debug)
			printf("(%f,%f)\r\n", x,y); // output values for debuging
		target_y = euler(step_size,target_x,x,y,func,debug); // do it again...
	}
	return target_y; // return the target_y value
}