The Numerical Study of Singularly Perturbed Differential-Difference Turning Point Problems: Twin Boundary Layers

P. Rai () and K. K. Sharma ()
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P. Rai: Panjab University, Department of Mathematics (Center for Advance Study in Mathematics)
K. K. Sharma: Panjab University, Department of Mathematics (Center for Advance Study in Mathematics)

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 285-292 from Springer

Abstract: Abstract A boundary value problem for singularly perturbed differential-difference equation with turning point is considered. Some a priori estimates are obtained on the solution and its derivatives. In general, to tackle such type of problems one encounters three difficulties: (i) due to presence of the turning point, (ii) due to presence of terms containing shifts and (iii) due to presence of the singular perturbation parameter. Due to presence of the singular perturbation parameter the classical numerical methods fail to give reliable numerical results and do not converge uniformly with respect to the singular perturbation parameter. In this paper a parameter uniform finite difference scheme is constructed to solve the boundary-value problem. A parameter uniform error estimate for the numerical scheme so constructed is established. Numerical experiments are carried out to demonstrate the efficiency of the numerical scheme and support the theoretical estimates.

Keywords: Finite Difference Scheme; Delay Differential Equation; Shishkin Mesh; Stochastic Delay Differential Equation; Shift Argument (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_31

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DOI: 10.1007/978-3-642-33134-3_31

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