Now showing items 1-20 of 140

      Authors Name
      Iahn, Roberta Cesarino [1]
      Iavarone, Ayşenur Hilal [1]
      Ifigeneial, Vamvakidou [1]
      Iftekharuddin, Khan [2]
      Ildız, Gülce Öğrüc [1]
      Ildız, Gülce Öğrüç [2]
      Ilgar, Rüştü [1]
      Ilgın, Hicran Özlem [2]
      Ilias, Michailidis [1]
      Ilıcak - Aydınalp, Ş. Güzin [1]
      Ilıcak, Güzin [1]
      Ilıcak, Ş. Güzin [1]
      Ilıcak, Şükran Güzin [1]
      In the thesis, the theory of analytic and harmonic functions are taken up first. Then the so-called log-harmonic functions are studied. Log-harmonic functions are basically those complex mappings having a harmonic logarithm, and they are represented as a multiplication of an analytic and a co-analytic function. The subclass Slh(A;B) of log-harmonic functions is introduced and studied. This is the subclass consisting of log-harmonic functions whose analytic part is a Janowski starlike. It should be noted that it is also possible to obtain new results provided that the analytic part of a log-harmonic function belongs to a well-known class of analytic functions. Distortion theorems for the functions in Slh(A;B), as well as for their analytic and co-analytic parts, are obtained.Marx-Strohhacker inequality and the radius of starlikeness for the class Slh(A;B) are derived. The Jacobian function and its distortion for the members of Slh(A;B) are obtained. Lastly, a coecient inequality is also obtained for the class Slh(A;B). [1]
      In this thesis the energy preserving average vector field (ABV) integrator was applied to the non-linear Schrödinger (NLS) equation and the discretized model is reduced by proper orthogonal decomposition (POD).Numerical results for one and two dimensional NLS and coupled NLS with periodic and soliton solutions confirm the converge rates of the POD reduced model. The reduced model preserves the Hamiltonian structure and is also energy preserving for coupled NLS dispersion analysis was also carried out. [1]
      In this thesis, numerical solutions of fractional partial differential equations and system of fractional ordinary differential equations are considered. Non-polynomial spline method and Galerkin finite element methods are applied for the equations above. Caputo fractional derivative is used for fractional derivative term. Taylor expansion is used to obtain M_i moments in spline method. In order to test accuracy of the spline method applied to fractional diffusion equation, numerical dispersion analysis is applied and useful results are obtained. It is concluded that in all the problems numerical results converge to the exact solutions when h goes to zero. It yields results compatible with the exact solutions and consistent with other existing numerical methods. Use of non-polynomial splines and Galerkin method have shown that they are applicable methods for this type of equations. [1]
      Inanc, N. [1]