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Title: The solution of some differential equations by nonstandard finite difference method
Authors: Tanoğlu, Gamze
Kıran Güçoğlu, Arzu
Issue Date: 2005
Publisher: Izmir Institute of Technology
Abstract: In this thesis, the nonstandard finite difference method is applied to construct thenew finite difference equations for the first order nonlinear dynamic equation, second order singularly perturbed convection diffusion equation and nonlinear reaction diffusion partial differential equation The new discrete representation for the first order nonlinear dynamic equation allows us to obtain stable solutions for all step-sizes.For singularly perturbed convection diffusion equation, the error analysis reveals that the nonstandard finite difference representation gives the better results for any values of the perturbation parameters. Finally, the new discretization for the last equation is obtained.The lemma related to the positivity and boundedness conditions required for the nonstandard finite difference scheme is stated. Numerical simulations for all differential equarions are illustrated based on the parameters we considered.
Description: Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2005
Includes bibliographical references (leaves: 55-57)
Text in English; Abstract: Turkish and English
ix, 66 leaves
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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