Too long for a comment: I think the list of references appearing on the wiki page for numerical methods for ordinary differential equations is not bad overall; let me just highlight some canonical references by (i) Ernst Hairer, Syvert Nørsett and Gerhard Wanner; (ii) Arieh Iserles; (iii) John Butcher; and (iv) C. William Gear.

(i) *Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard*, Solving ordinary differential equations. I: Nonstiff problems., Springer Series in Computational Mathematics 8. Berlin: Springer (ISBN 978-3-642-05163-0/pbk). xv, 528 p. (2010). ZBL1185.65115.

(ii) *Iserles, Arieh*, A first course in the numerical analysis of differential equations, Cambridge Texts in Applied Mathematics. Cambridge: Cambridge Univ. Press. 400 p. (1995). ZBL0841.65001.

(iii) *Butcher, J. C.*, Numerical methods for ordinary differential equations., Chichester: Wiley (ISBN 0-471-96758-0/hbk). xiv, 425 p. (2003). ZBL1040.65057.

(iv) *Gear, C. William*, Numerical initial value problems in ordinary differential equations., Englewood Cliffs, NJ: Prentice-Hall. xvii, 253 p. (1971). ZBL1145.65316.