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Wondwosen Gebeyaw Melesse,Awoke Andargie Tiruneh,Getachew Adamu Derese 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.1
In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.
MELESSE, WONDWOSEN GEBEYAW,TIRUNEH, AWOKE ANDARGIE,DERESE, GETACHEW ADAMU The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.1
In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.
DAGNACHEW MENGSTIE TEFERA,AWOKE ANDARGIE TIRUNEH,GETACHEW ADAMU DERESE 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
This paper is concerned with singularly perturbed convection-diffusion parabolic partial differential equations which have time-delayed. We used the Crank-Nicolson(CN) scheme to build a fitted operator to solve the problem. The underling method's stability is investigated, and it is found to be unconditionally stable. We have shown graphically the unstableness of CN-scheme without fitting factor. The order of convergence of the present method is shown to be second order both in space and time in relation to the perturbation parameter. The efficiency of the scheme is demonstrated using model examples and the proposed technique is more accurate than the standard CN-method and some methods available in the literature, according to the findings.