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.