This is a preview of subscription content, log in via an institution to check access.
References
N. S. Bakhvalov, “On optimisation of methods for solving boundary value problems in the pressence of a boundary layer,” Zh. Vychisl. Mat. i Mat. Fiz.,9, No. 4, 841–859 (1969).
V. D. Liseîkin and V. E. Petrenko, “On numerical solution of nonlinear singularly perturbed problems,” Dokl. Akad. Nauk SSSR,297, No. 4, 791–794 (1987).
B. M. Bagaev, “The Galërkin method for an ordinary differential equation with a small parameter,” Chyslennye Metody Mekhaniki Sploshnoî Sredy,10, No. 1, 5–16 (1979).
N. A. Blatov, “Convergence in uniform norm of the Galërkin method for a nonlinear singular perturbed problem,” Zh. Vychisl. Mat. i Mat. Fiz.,26, No. 8, 1175–1188 (1986).
V. D. Liseîkin, “On numerical solution of equations with polynomial boundary layer,” Zh. Vychisl. Mat. i Mat. Fiz.,26, No. 12, 1813–1820 (1986).
T. C. Hanks, “A model relating heat-flow values near and vertical velocities of mass transport beneath oceanic rises,” J. Geophys. Res.,76, No. 2, 537–544 (1971).
S. B. Angenent, L. A. Mallet-Paret, and L. A. Peletier, “Stable transition layer in a semilinear boundary value problem,” J. Differential Equations,67, 212–242 (1987).
P. Ya. Polubarinova-Kochina, Theory of Motion of Phreatic Water [in Russian], Nauka, Moscow (1977).
K. K. Zamaraev, P. F. Khaîrutdinov, and V. P. Zhdanov, Electron Tunneling in Chemistry. Chemical Reactions at Large Distances [in Russian], Nauka, Novosibirsk (1985).
N. N. Brish, “On boundary value problems for the equation εy″=f(y,y ′,x) with ε small,” Dokl. Akad. Nauk SSSR,155, No. 3, 429–432 (1954).
V. D. Liseîkin, “On numerical solution of a singularly perturbed turning point equation,” Zh. Vychisl. Mat. i Mat. Fiz.,24, No. 12, 1812–1818 (1984).
F. E. Berger, H. Han, and R. B. Kellog, “A priori estimates of a numerical method for a turning point problem,” Math. Comp.,42, 465–492 (1984).
A. E. Berger, “A note concerning the El-Mistikawi-Werle exponential finite difference scheme for a boundary turning point problem,” in: Proc. Third International Conference on Boundary and Interior Layers, Dublin, 1984, pp. 67–80.
A. A. Dorodnitsyn, “Asymptotic laws of the distribution of eigenvalues for some particular types of the second order differential equations,” Uspekhi Mat. Nauk,7, No. 6, 3–96 (1952).
M. A. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentis Hall, Eglewood Cliffs (1967).
V. D. Liseîkin and V. E. Petrenko, An Adaptive-Invariant Method for Numerical Solution of Problems with Boundary and Interior Layers, Novosibirsk (1989).
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 6, pp. 106–117, November–December, 1992.
Translated by T. N. Rozhkovskaya
Rights and permissions
About this article
Cite this article
Liseîkin, V.D. Estimates for derivatives of solutions to differential equations with boundary and interior layers. Sib Math J 33, 1039–1051 (1992). https://doi.org/10.1007/BF00971027
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971027