Browsing by Author "Yurtsever H.A."

Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    Perturbative derivation and comparisons of root-finding algorithms with fourth order derivatives
    (Association for Scientific Research, 2007) Pakdemirli M.; Boyaci H.; Yurtsever H.A.
    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. © Association for Scientific Research.
  • No Thumbnail Available
    Item
    Estimating roots of polynomials using perturbation theory
    (2007) Pakdemirli M.; Yurtsever H.A.
    Perturbation theory and the order of magnitude of terms are employed to develop two theorems. The theorems may be useful to estimate the order of magnitude of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special types of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theorems are presented as examples. © 2006 Elsevier Inc. All rights reserved.
  • No Thumbnail Available
    Item
    A root-finding algorithm with fifth order derivatives
    (Association for Scientific Research, 2008) Pakdemirli M.; Boyaci H.; Yurtsever H.A.
    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. © Association for Scientific Research.
  • No Thumbnail Available
    Item
    An application of calculus: Optimum parabolic path problem
    (Oxford University Press, 2009) Atasever M.; Pakdemirli M.; Yurtsever H.A.
    A practical and technological application of calculus problem is posed to motivate freshman students or juniory high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object for which the work done by variable coefficient air friction force is minimum is determined. If a flying object follows the determined path, energy requirement would be less compared with other parabolic or linear paths. © The Author 2009. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved.