BLOCK METHOD APPROACH FOR COMPUTATION OF ERRORS OF SOME ADAMS CLASS OF METHODS.

Abstract

Traditionally, the error and order constant of block linear multistep methods were analyzed by examining each block members separately. This paper proposes a block-by-block analysis of the schemes as they appear for implementation. Specifically, cases when k= 2, 3, 4, and 5 for Adams Moulton (implicit) are reformulated as continuous schemes in order to generate a sufficient number of schemes required for the methods to be self-starting. The derivation was accomplished through the continuous collocation technique utilizing power series as the basis function, and the property of order and error constants is examined across the entire block for each case of the considered step number. The findings of the study generated error constants in block form for Adams Bashforth and Adams Moulton procedures at steps 2, 3, 4, 5 k  . Furthermore, the relevance of the study demonstrates that calculating all members' error constants at once, reduces the amount of time necessary to run the analysis. The new approach, for examining the order and error constants of a block linear multistep method, is highly recommended for application in solving real-world problems, modelled as ordinary and partial differential equations.