Browsing by Author "H. BOYACI"

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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.
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    A new perturbation algorithm with better convergence properties: Multiple scales lindstedt poincare method
    (2009) H. BOYACI; M. PAKDEMİRLİ; M. M. F. KARAHAN
    A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities.
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    Forced vibrations of strongly nonlinear systems with multiple scales Lindstedt Poincare method
    (2011) M. PAKDEMİRLİ; H. BOYACI; M. M. F. KARAHAN
    Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement.