Browsing by Author "H. A. YURTSEVER"

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    Perturbative derivation and comparisons of root-finding algorithms with fourth order derivatives
    (2007) H. BOYACI; M. PAKDEMİRLİ; H. A. YURTSEVER
    Perturbation theory is systematically used to generate root finding algorithms with fourth order derivatives. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding formulas can be generated. Expanding Taylor series up to fourth order derivatives and taking two, three and four correction terms in the perturbation expansions, three different root finding algorithms are derived. The algorithms are contrasted numerically with each other as well as with the Newton-Raphson algorithm. It is found that the quadruple-correction-term algorithm performs better than the others.
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    A root-finding algorithm with fifth order derivatives
    (2008) H. BOYACI; H. A. YURTSEVER; M. PAKDEMİRLİ
    Perturbation theory is used to generate a root finding algorithm with fifth order derivatives. The algorithm is called Quintuple-Correction-Term algorithm. The new algorithm is contrasted with the previous Quadruple-Correction-Term and Triple- Correction-Term algorithms in the literature. It is found that adding a fifth correction term in the algorithm does not improve the performance.