Hi: We needed those methods for a college project and we implemented them with GSL, I know Euler and Improved Euler are merely didactic methods but maybe some students (like us) could avoid reinventing the wheel. On the other hand, 4 step Adams-Bashford-Moulton method could be usable in a real application. We used Runge-Kutta to obtain the remainig three initial steps. I attached the 3 files just in case you want to include them in the GSL distribution Cheers Alfonso Acosta PS: The three methods were tested without step control, so we are not sure wether the error we provide is correct or not.