Abstract
This article constructed and implemented a family of a third derivative trigonometric fitted method of order k+3 whose coefficients are functions of frequency and step size for the integration of systems of first-order stiff and periodic Initial Value Problems. The Block Third Derivative Trigonometric Fitted methods (BTDTFMs) are constructed via multistep collocation technique and applied in block form as simultaneous numerical integrators which make them self-starting. The convergence, accuracy, and efficiency of the methods are established through some standard numerical examples.
Highlights
Many numerical methods have been developed along these problems but put stark limitations on the choice of suitable three directions which include but not limited to Gear [3], Enmethods for stiff problems
Dahlquist [1] established that the right [4], Cash [5], Wu [6], Hojjati [7], Jator [8], Sahi et al [9], most accurate A-stable linear multistep method has order 2
Since each Block Third Derivative Trigonometric Fitted methods (BTDTFMs) is of order p ≥ 5 > 1,as shown in Table 1, it is consistent (Lambert [57] and Fatunla [58])
Summary
The idea of using basis function which integrates a set of linearly independent function exactly other than polynomial can be traced to the work of Gautchi [26] and Lyche [27] Many of such extension has been discussed in Coleman and Duxbury [28], Ixaru et al [29], Vanden Berghe and his collaborators ([24], [30,31]), Simos [32,33], Tsitouras and Simos [34], Nguyen et al [35], Senu et al [36], Jator and his collaborators [37,38,39,40,41], Jator [42] and Abdulganiy and his collaborators [43,44,45].
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