Open AccessA Family of Second Derivative Simpson’s Type Block Methods for Stiff Systems
Author(s) -
Yohanna Sani Awari,
Shikaa Samuel,
Stephen Nengem Mkegh
Publication year - 2020
Publication title -
journal of advance research in mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2208-2409
DOI - 10.53555/nnms.v7i9.864
Subject(s) - linear multistep method , ode , mathematics , block (permutation group theory) , ordinary differential equation , property (philosophy) , solver , stability (learning theory) , stiff equation , derivative (finance) , type (biology) , l stability , mathematical analysis , differential equation , computer science , mathematical optimization , geometry , differential algebraic equation , philosophy , ecology , epistemology , machine learning , financial economics , economics , biology
In this paper, we developed a new family of self starting second derivative Simpson’s type block methods (SDSM) of uniform order for step number. The new block methods forwere seen to possess good stability property as they possessed good regions of absolute stability. They were also found to be consistent, zero stable and A-stable (Fig.4). This essential property made them suitable for the solution of stiff system of ordinary differential equations. Four numerical examples were considered and results obtained show improved accuracy in terms of their Maximum absolute errors when compared with the work of existing scholars. The newly developed block methods were seen to approximate well with the stiff Ode Solver (Fig. 5, 6, 7 and 8).