Gamze Tanoglu

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We provide an error analysis of the operator splitting method of the Lie-Trotter type applied to the Burgers-Huxley equation ut +αuux − εuxx = β (1−u)(u− γ)u. We show that the Lie-Trotter splitting method converges with the expected rate in Hs(R), where Hs(R) is the Sobolev space and s is an arbitrary nonnegative integer. We split the equation into linear(More)
In this paper, we contribute higher order operator-splitting method improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order operator-splitting methods is presented. While applying the methods to partial differential equations, the benefits of balancing time and(More)
In this thesis, the nonstandard finite difference method is applied to construct the new 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(More)
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