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Differential quadrature method for singularly perturbed differential-difference equations with small delay in convection term

H.S. Prasad1 and  Y.N. Reddy2*

1Department of Mathematics, National Institute ofTechnology, Jamshedpur, INDIA

2*Department Mathematics, National Institute of Technology, Warangal, INDIA. e-mail: ynreddy_nitw@yahoo.com

Abstract:  

In this paper, DifferentialQuadrature Method (DQM) is presented for finding the numerical solution of singularly perturbed differential-difference equations with small delay in convection term. Such problems are associated with the study of bistable devices, variational problems in control theory and the first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. The Differential Quadrature Method is an efficient descritization technique in solving initial and /or boundary value problems accurately using a considerably small number of non-uniform grid points. We have used the Lagrange’s interpolation technique to interpolate the solution values at uniform points. The derived Lagrange’s interpolation polynomial is capable of producing almost the same accuracy as obtained in the DQM solution at non-uniform grid points. To demonstrate the applicability of these methods, we have solved the model example problems and compared the computational results with the exact solutions. Comparisons showed that the method is capable of producing highly accurate results with high efficiency.

Keywords: Differential-difference equations; Differential Quadrature Method; Singular perturbation; Boundary value problem; Boundary layer

 

 

 

 

 

International eJournal of Mathematical Sciences, Technology and Humanities

Volume 5, Issue 1, Pages:  6 - 25