The numerical solution of second-order boundary value problems on nonuniform meshes

Mathematics of Computation

Volumn 47, Issue 176, 1986, Pages 511-535

  Manteuffel, Thomas A ^a   White, Andrew B ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966240649     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0856700-3     Document Type: Article

References (23)

1. C. M. Ablow & S. Schechter, "Campylotropic Coordinates, " J. Comput. Phys., v. 27, 1978, pp. 351-362.
2. T. H. Chong, " A variable mesh finite différence method for solving a dass of parabolic differential équations in one space variable, " SIAM J. Numer. Anal., v. 15, 1978, pp. 835-857.
3. MELVYN CIMENT, STEPHEN W. LEVENTHAL & BERNARD C. WEINBERG, "The operator compact implicit method for parabolic équations, " J. Comput. Phys., v. 28, 1978, pp. 135-166.
4. Stephen F. Davis & Joseph E. Flaherty, "An adaptive finite element method for initial-boundary value problems for partial differential équations, " SIAM J. Sci. Statist. Comput., v. 3, 1982, pp. 6-27.
5. V. E. Denny & R. B. Landis, "A new method for solving two-point boundary value problems using optimal node distribution, " J. Comput. Phys., v. 9, 1972, pp. 120-137.
6. Eusebius J. Doedel, "The construction of finite différence approximations to ordinary differential équations, " SIAM J. Numer. Anal., v. 15, 1978, pp. 450-465.
7. Eusebius J. Doedel, " Finite différence methods for nonlinear two-point boundary value problems, " SI A M J. Numer. Ana/., v. 16, 1979, pp. 173-185.
8. ROLF D. GRIGORIEFF, "Some stability inequalities for compact finite différence schemes, " type-script.
9. J. D. Hoffman, "Relationship between the truncation errors of centered finite-difference ap-proximations on uniform and nonuniform meshes, " J. Comput. Phys., v. 46, 1982, pp. 469-474.
10. EUGENE ISAACSON & H. B. KELLER, Analysis of Numerical Methods, Wiley, New York, 1966.
11. HERBERT B. KELLER, "Accurate différence methods for linear ordinary differential systems subject to linear constraints, " SIAM J. Numer. Anal., v. 6, 1969, pp. 8-30.
12. H. B. Keller & A. B. White, "Différence methods for boundary' value problems in ordinary" differential équations, " SIAM J. Numer. Anal., v. 12, 1975, pp. 791-802.
13. HERBERT B. KELLER, Numerical Solution of Two Point Boundary' Value Problems, SIAM, Regional Conference Series in Applied Mathematics, 24.
14. H.-O. KREISS, "Différence approximations for boundary and eigenvalue problems for ordinary differential équations, " Math. Comp., v. 26, 1972, pp. 605-624.
15. H.-O. KREISS, T. A. MANTEUFFEL, B. SWARTZ, B. WENDROFF & A. B. WHITE, JR., "Supra-conver-gent schemes on irregular grids, " Math. Comp., v. 47, 1986, pp. 537-554.
16. DAVID LEVERMORE, private communication.
17. R. E. LYNCH & J. R. RICE, The HODIE method, Report C5D-TR 188, Dept. of Computer Science, Purdue University, W. Lafayette, Indiana.
18. T. A. MANTEUFFEL & A. B. WHITE, "On the efficient solution of systems of second-order boundary value problems, " SIAM J. Numer. Anal. (To appear.)
19. M. R. OSBORNE, "Minimizing truncation error in finite différence approximations to ordinary differential équations, " Math. Comp., v. 21, 1967, pp. 133-145.
20. CARL E. PEARSON, "On a differential équation of boundary layer type, " J. Math. Phys., v. 47, 1968, pp. 134-154.
21. Blair K. Swartz, "The construction and comparison of finite différence analogs of some finite element schemes, " in Mathematical Aspects of Finite Elements Partial Differential Equation (1974).
22. A. N. TIKHONOV & A. A. SAMARSKII, "Homogeneous différence schemes on nonuniform nets, " Zh. Vychisl. Mat. i Mat. Fiz., v. 1, 1962, English translation (Russian).
23. A. B. White, Jr., "On selection of equidistributing meshes for two-point boundary value problems, " SIAM J. Numer. Anal., v. 16, 1979, pp. 472-502.