We consider singularly perturbed boundary-value problems in the case of boundary layers. To find approximate solutions of these problems, we use a collocation method based on cubic splines of minimal defect on nonuniform meshes.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
G. I. Marchuk and V. I. Agoshkov,Introduction to Projective Mesh Techniques [in Russian], Nauka, Moscow (1981).
A. M. Samoilenko and N. I. Ronto,Numerical Analytic Methods for Investigation of Solutions of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1986).
I. A. Blatov and V. V. Strygin, “Convergence of the spline collocation method on optimal meshes for singularly perturbed boundary-value problems,”Differents. Uravn.,24, No. 11, 1977–1987 (1988).
I. A. Blatov and V. V. Strygin,Convergence of the Collocation Method for Singularly Perturbed Boundary-Value Problems [in Russian], Deposited in VINITI No.4710-B87, Voronezh (1987).
I. A. Blatov and V. V. Strygin, “Convergence of the spline collocation method for singularly perturbed boundary-value problems on locally uniform meshes,”Differents. Uravn.,26, No. 7, 1191–1197 (1990).
A. B. Vasil'eva and V. F. Butuzov,Asymptotic Expansion of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).
N. S. Bakhvalov, “On optimization of methods for solution of problems with a boundary layer,”Zh. Vych. Mat. Mat. Fiz.,9, No. 4, 841–859 (1969).
S. A. Lomov,Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).
Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko,Spline Function Techniques [in Russian], Nauka, Moscow (1980).
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 411–417, April, 1994.
About this article
Cite this article
Strygin, V.V., Blatov, I.A. & Pokornaya, I.Y. Collocation method for solving singularly perturbed boundary-value problems by using cubic splines. Ukr Math J 46, 433–440 (1994). https://doi.org/10.1007/BF01060413
- Boundary Layer
- Approximate Solution
- Collocation Method
- Nonuniform Mesh
- Minimal Defect