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On the numerical integration of a class of singular perturbation problems. (English) Zbl 0633.65075
A three-point difference scheme recently proposed by M. K. Kadalbajoo and Y. N. Reddy [ibid. 51, 441-452 (1986; Zbl 0579.65081)] for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to one- sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.
Reviewer: N.K.Nichols

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
Full Text: DOI
[1] Kadalbajoo, M. K., andReddy, Y. N.,Numerical Integration of a Class of Singular Perturbation Problems, Journal of Optimization Theory and Applications, Vol. 5, pp. 441-452, 1986. · Zbl 0579.65081 · doi:10.1007/BF00940284
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