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  1. 3 Acta Physica Polonica A

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  1. 3 2014

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  1. 3 Caglar H.

  2. 3 Caglar N.

  3. 3 Ozer M.

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B-Spline Solution and the Chaotic Dynamics of Troesch's Problem

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Caglar H., Caglar N., Ozer M.
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vol. 125
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issue 2
554-560
EN
A B-spline method is presented for solving the Troesch problem. The numerical approximations to the solution are calculated and then their behavior is studied and commenced. The chaotic dynamics exhibited by the solutions of Troesch's problem as they were derived by the decomposition method approximation are examined and an approximate critical value for the parameter λ is introduced also in this study. For the parameter value slightly less than λ ≈ 2.2, the solutions begin to show successive bifurcations, finally entering chaotic regimes at higher λ values. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where the first bifurcation occurs.
2
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The Numerical Solution of Fractional Diffusion Equation by Using Local Polynomial Regression

100%
Caglar H., Caglar N., Ozer M.
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vol. 125
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issue 2
551-553
EN
In this paper, we apply the local polynomial regression for the solution of the one-dimensional fractional diffusion equation. The Caputo fractional derivative is used for the formulation. A numerical example is given to show the application of the present method. The effect of the fractional order (α) of the equation is illustrated by changing α from 1.01 to 1.99.
3
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B-Spline Solution for a Convection-Diffusion Equation

100%
Caglar H., Caglar N., Ozer M.
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vol. 125
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issue 2
548-550
EN
This paper is concerned with the numerical solution of the convection diffusion problems. A family of B-spline methods has been considered for the numerical solution of the problems. The results showed that the present method is an applicable technique and approximates the exact solution.
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