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http://dx.doi.org/10.14317/jami.2022.491

FITTED OPERATOR ON THE CRANK-NICOLSON SCHEME FOR SOLVING A SMALL TIME DELAYED CONVECTION-DIFFUSION EQUATIONS  

TEFERA, DAGNACHEW MENGSTIE (Department of Mathematics, College of Sciences, Bahir Dar University)
TIRUNEH, AWOKE ANDARGIE (Department of Mathematics, College of Sciences, Bahir Dar University)
DERESE, GETACHEW ADAMU (Department of Mathematics, College of Sciences, Bahir Dar University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.3_4, 2022 , pp. 491-505 More about this Journal
Abstract
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.
Keywords
Singularly perturbed; Crank-Nicolson method; fitted operator; convection-diffusion;
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