The solution of some differential equations by nonstandard finite difference method
Title:
The solution of some differential equations by nonstandard finite difference method
Author:
Kıran Güçoğlu, Arzu.
Personal Author:
Publication Information:
[s.l.]: [s.n.], 2005.
Physical Description:
ix, 66 leaves.: ill.+ 1 computer laseroptical disc.
General Note:
Keywords: Nonlinear differential equations, finite difference method, numeric simulation.
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.
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Thesis (Master)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Master).
Electronic Access:
Access to Electronic Version.