The 7 and 8 Families of Hybrid Block Methods for Numerical Solution of Initial Value Problems in Stiff Equations

An independent hybrid block Simpson’s methods with a very closely accurate members of order p=q+2 as a block was formulated. This was obtained through increasing the number k in the multi-step collocation (MC). Maple software was used to facilitate the derivation of the k-step continuous formulae for k=6 and 7. In this paper, one off-grid collocation point was added in the MC in-between the last two step sizes, to get the desirable schemes. These schemes were evaluated for simultaneous application on stiff equations. The numerical results obtained signified the efficiency of the schemes.