International Journal of Engineering, Science and Mathematics

This paper discusses the effect of simultaneously increase in step-number (k) and order of derivative (l) on the accuracy of an implicit multiderivative method. The study varied k and l simultaneously from 1–4 to produce some variants of the method. These variants were implemented by using them to solve two initial value problems of first order ordinary differential equations. A comparative study of the computed results was carried out which showed an improvement in accuracy as k and l increased from k=1; l =1 to k=2; l =2 but accuracy reduced from k=3; l =3 to k=4; l =4, suggesting that two step second derivative scheme (k=2; l=2) has optimal accuracy when k and l were increased simultaneously.