Generalized OCI Schemes for Boundary Layer Problems

Berger, Alan E.; Solomon, Jay M.; Ciment, Melvyn; Leventhal, Stephen H.; Weinberg, B. C.

doi:10.2307/2006188

Cited by 26 publications

(42 citation statements)

References 15 publications

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“…These conditions were first proposed for the case of uniform mesh in [1]. From the conditions (3.6) and (3.7), we get …”

Section: Description Of the Methodsmentioning

confidence: 99%

High-order uniformly convergent method for nonlinear singularly perturbed delay differential equations with small shifts

Salama¹,

Alamery²

2016

Turk J Math

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In this paper, we propose and analyze a high-order uniform method for solving boundary value problems (BVPs) for singularly perturbed nonlinear delay differential equations with small shifts (delay and advance). Such types of BVPs play an important role in the modeling of various real life phenomena, such as the variational problem in control theory and in the determination of the expected time for the generation of action potentials in nerve cells. To obtain parameter-uniform convergence, the present method is constructed on a piecewise-uniform Shishkin mesh. The error estimate is discussed and it is shown that the method is uniformly convergent with respect to the singular perturbation parameter. Moreover, a bound of the global error is also derived. The effect of small shifts on the solution behavior is shown by numerical computations. Several numerical examples are presented to support the theoretical results, and to demonstrate the efficiency and the high-order accuracy of the proposed method.

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“…These conditions were first proposed for the case of uniform mesh in [1]. From the conditions (3.6) and (3.7), we get …”

Section: Description Of the Methodsmentioning

confidence: 99%

High-order uniformly convergent method for nonlinear singularly perturbed delay differential equations with small shifts

Salama¹,

Alamery²

2016

Turk J Math

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show abstract

“…To prove this theorem we adopt the comparison function approach, which was employed in [14,15,16] for analysis of some difference methods for singular perturbation problems. An outline is given in [15].…”

Section: Convergencementioning

confidence: 99%

“…An outline is given in [15]. For our problem we choose the comparison functions ϕ(x) = 1+x and ψ(x) = exp(− λD −1 (1 − x)) for some λ > 0.…”

Section: Convergencementioning

confidence: 99%

The complete flux scheme—Error analysis and application to plasma simulation

Liu

Dijk

Boonkkamp

et al. 2013

Journal of Computational and Applied Mathematics

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“…The present paper is concerned with finite-difference approximations, which have received their share of attention (see, for example, [7], [8], [13], [17], and [20] and references contained therein). A continuous source of analyses of various approaches to these problems is supplied by the proceedings of the BAIL conferences edited by J. J. H. Miller [22], [23], and [24].…”

mentioning

confidence: 99%