This study is considered to formulate Mathematica pseudocodes for
implementing block Adams family (MPIBAF). An idea multinomial basis
function approximant will be utilized to process the interpolation and
collocation methods. A special block Adams family in form of block
Adams-Bashforth and Block Adams-Moulton methods will be developed via
interpolation and collocation method to foster the principal local
truncation error thereby bringing into existence the convergency limits.
The application of Mathematica pseudocodes will be processed on some
applied math problems in a parallel manner with each processor depending
on one another. The computable results will be produced via a compiled
Mathematica pseudocode in a gradual manner. In addition, technical
computation supersedes manual computation as demonstrated by the results
of the numerous gains such as ease of computable processes and
structures, better accuracy and quicker convergency.