A Family of Second Derivative Simpson’s Type Block Methods for Stiff Systems - Awari, Yohanna; Samuel, Shikaa; Mkegh, Stephen Nengem (Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 2020)
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).