Browsing by Author "Akkoyunlu, Canan"
Now showing items 1-14 of 14
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Average Vector Field Splitting Method for Nonlinear Schrodinger Equation
(Springer-Verlag Berlin, Heidelberger Platz 3, D-14197 Berlin, Germany, 2013)The energy preserving average vector field integrator is applied to one and two dimensional Schrodinger equations with symmetric split-step method. The numerical results confirm the long-term preservation of the Hamiltonians, ... -
Energy preserving integration of the strongly coupled nonlinear Schrodinger equation
(Amer Inst Physics, 2 Huntington Quadrangle, Ste 1No1, Melville, Ny 11747-4501 USA, 2015)In this paper, average vector field method (AVF) is derived for strongly coupled Schrodinger equation (SCNLS). The SCNLS equation is discretized in space by finite differences and is solved in time by structure preserving ... -
Lineer olmayan schrödinger denkleminin enerji korumalı yöntemle çözümü ve model indirgeme yönteminin uygulanması
(İstanbul Kültür Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Bilgisayar Anabilim Dalı, 2013-07)Bu tezde lineer olmayan Schrödinger (NLS) denklemi enerji koruma özelliğine sahip ortalama vektör alanı (OVA) ile çözülmüştür. Ayrıca model indirgeme yöntemi olarak uygun dik ayrışım (UDA) yöntemi uygulanarak bir ve iki ... -
Model order reduction for nonlinear Schrodinger equation
(Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 USA, 2015-05-01)We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure ... -
Non Polynomial Spline Solution for a Fourth Order Non Homegeneous Parabolic Partial Differential Equation with a Seperated Boundary
(2012)In this paper, a fourth-order non-homogeneous parabolic partial differential equation with initial and separated boundary conditions is solved by using a non-polynomial spline method. In the solution of the problem, finite ... -
Non-Polynomial Spline Method for Fractional Diffusion Equation
(Eudoxus Press, Llc, 1424 Beaver Trail Drive, Cordova, Tn 38016 Usa, 2012-11)The one-dimensional fractional diffusion equation is studied systematically using the non-polynomial spline method. The Caputo fractional derivative is used for formulation. An example is solved to assess the accuracy of ... -
Non-Polynomial Spline Method Of A Non-Linear System Of Second-Order Boundary Value Problems
(Eudoxus Press, Llc, 1424 Beaver Trail Drive, Cordova, Tn 38016 Usa, 2010-04)The non-polynomial spline method is proposed to solve a non-linear system of the second-order boundary value problems (BVPs). Some numerical results are given to demostrate the validity and applicability of the presented ... -
Non-polynomial Spline Solution for a Fourth-Order Non-homogeneous Parabolic Partial Differential Equation with a Separated Boundary Condition
(Springer-Verlag Berlin, Heidelberger Platz 3, D-14197 Berlin, Germany, 2013)In this paper, a fourth-order non-homogeneous parabolic partial differential equation with initial and separated boundary conditions is solved by using a non-polynomial spline method. In the solution of the problem, finite ... -
The numerical solution of the singular two-point boundary value problems by using non-polynomial spline functions
(2010)The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results ...
