1. Several improvements of the 2-point third order midpoint iterative method using weight functions
- Author
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Babajee, Diyashvir Kreetee Rajiv
- Subjects
- *
MATHEMATICAL functions , *ITERATIVE methods (Mathematics) , *ROBUST control , *PROOF theory , *APPLIED mathematics , *NUMERICAL analysis - Abstract
Abstract: In this paper, we improve the order of the Midpoint iterative method from three to four with same number of function evaluations using weight functions to obtain a class of 2-point fourth order Jarratt-type methods. Then we prove a general result to further improve the order of the old methods through an additional function evaluation using weight functions. In this way, we develop two 3-point sixth order midpoint methods using different weights. A family of n-point I.F.s of order 2n is proposed. Using weight functions, we further improve the methods to obtain a 5-point sixteenth order midpoint method with same efficiency index as the optimal 2-point fourth order Jarratt-type methods. Two numerical examples using different starting are provided to test the robustness of the methods. [Copyright &y& Elsevier]
- Published
- 2012
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