Numerical solution of singularly perturbed boundary-value problems using adaptive spline functions approximation

K. Surla

Authors

K. Surla Institute of Mathematics, Novi Sad, Serbia

Abstract views: 141

Abstract

Not available.

Downloads

Download data is not yet available.

References

Berger, Alan E.; Solomon, Jay M.; Ciment, Melvyn; Leventhal, Stephen H.; Weinberg, Bernard C. Generalized OCI schemes for boundary layer problems. Math. Comp. 35 (1980), no. 151, pp. 695-731, MR0572850, https://doi.org/10.1090/s0025-5718-1980-0572850-8

Berger, Alan E.; Solomon, Jay M.; Ciment, Melvyn An analysis of a uniformly accurate difference method for a singular perturbation problem. Math. Comp. 37 (1981), no. 155, pp. 79-94, MR0616361, https://doi.org/10.1090/s0025-5718-1981-0616361-0

Boglaev, I. P., A variational difference scheme for a boundary value problem with a small parameter multiplying the highest derivative. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 21 (1981), no. 4, 887-896, 1069, MR0630072.

Chin, R. C. Y.; Krasny, R. A hybrid asymptotic-finite element method for stiff two-point boundary value problems. SIAM J. Sci. Statist. Comput. 4 (1983), no. 2, pp. 229-243, MR0697177, https://doi.org/10.1137/0904018

Doolan, E. P.; Miller, J. J. H.; Schilders, W. H. A. Uniform numerical methods for problems with initial and boundary layers. Boole Press, Dún Laoghaire, 1980. xv+324 pp. ISBN: 0-906783-02-X, MR0610605.

Emel'janov, K. V. A difference scheme for an ordinary differential equation with a small parameter. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 18 (1978), no. 5, pp. 1146-1153, 1355, MR0515356.

Flaherty, Joseph E.; Mathon, William Collocation with polynomial and tension splines for singularly-perturbed boundary value problems. SIAM J. Sci. Statist. Comput. 1 (1980), no. 2, pp. 260-289, MR0594760, https://doi.org/10.1137/0901018

de Groen, P. P. N.; Hemker, P. W. Error bounds for exponentially fitted Galerkin methods applied to stiff two-point boundary value problems. Numerical analysis of singular perturbation problems (Proc. Conf., Math. Inst., Catholic Univ., Nijmegen, 1978), pp. 217-249, Academic Press, London-New York, 1979, MR0556520.

Il'in, A. M. A difference scheme for a differential equation with a small parameter multiplying the highest derivative. (Russian) Mat. Zametki 6 1969, pp. 237-248, MR0260195.

Il'in, V. P. Spline solutions of ordinary differential equations. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 18 (1978), no. 3, pp. 620-627, 811, MR0502369.

Jain, M. K.; Aziz, Tariq Numerical solution of stiff and convection-diffusion equations using adaptive spline function approximation. Appl. Math. Modelling 7 (1983), no. 1, pp. 57-62, MR0699824, https://doi.org/10.1016/0307-904x(83)90163-4

Kellogg, R. Bruce; Tsan, Alice Analysis of some difference approximations for a singular perturbation problem without turning points. Math. Comp. 32 (1978), no. 144, pp. 1025-1039, MR0483484, https://doi.org/10.1090/s0025-5718-1978-0483484-9

Lorenz, Jens Stability and consistency analysis of difference methods for singular perturbation problems. Analytical and numerical approaches to asymptotic problems in analysis (Proc. Conf., Univ. Nijmegen, Nijmegen, 1980), pp. 141-156, North-Holland Math. Stud., 47, North-Holland, Amsterdam-New York, 1981, MR0605505, https://doi.org/10.1016/s0304-0208(08)71107-1

Riordan, E.O., Singularly Perturbed Finite Element Methods, Numer. Math. 44 (1984), pp. 425-434, https://doi.org/10.1007/bf01405573

Surla, Katarina Accuracy increase for some spline solutions of two-point boundary value problems. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 14 (1984), no. 1, pp. 51-61, MR0786811.

Surla, K. A uniformly convergent spline difference scheme for a singular perturbation problem. Z. Angew. Math. Mech. 66 (1986), no. 5, pp. 328-329, MR0849981.

Zavyalov, Yu. S., Kvasov, B. I., Miroshnigenko, V. L. cyr Metody splaĭn-funktsiĭ. (Russian) [Methods of spline-functions] "Nauka", Moscow, 1980. 352 pp. (errata insert). 65-01 (65D07), MR0614595.