A comparison of global methods for linear two-point boundary value problems

Russell, R. D.; Varah, J. M.

doi:10.1090/S0025-5718-1975-0388788-3

A comparison of global methods for linear two-point boundary value problems
HTML articles powered by AMS MathViewer

by R. D. Russell and J. M. Varah PDF

Math. Comp. 29 (1975), 1007-1019 Request permission

Comment: Math. Comp. 31 (1977), 916-921.

Abstract:

Recently there has been a great deal of interest in numerical methods of a global nature for boundary value problems. In this paper we discuss and compare these global methods from a computational point of view, for the case of a single linear two-point boundary value problem.

References

J. H. Bramble and A. H. Schatz, On the numerical solution of elliptic boundary value problems by least squares approximation of the data, Numerical Solution of Partial Differential Equations, II (SYNSPADE 1970) (Proc. Sympos., Univ. of Maryland, College Park, Md., 1970) Academic Press, New York, 1971, pp. 107–131. MR 0273837
Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. MR 373328, DOI 10.1137/0710052
R. J. Herbold, M. H. Schultz, and R. S. Varga, The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques, Aequationes Math. 3 (1969), 247–270. MR 261798, DOI 10.1007/BF01817445
J. Nitsche, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math. 11 (1968), 346–348 (German). MR 233502, DOI 10.1007/BF02166687
Martin H. Schultz, Quadrature-Galerkin approximations to solutions of elliptic differential equations, Proc. Amer. Math. Soc. 33 (1972), 511–515. MR 315919, DOI 10.1090/S0002-9939-1972-0315919-2
Martin H. Schultz, Spline analysis, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0362832
Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0443377
J. M. Varah, On the solution of block-tridiagonal systems arising from certain finite-difference equations, Math. Comp. 26 (1972), 859–868. MR 323087, DOI 10.1090/S0025-5718-1972-0323087-4
James M. Varah, A comparison of some numerical methods for two-point boundary value problems, Math. Comp. 28 (1974), 743–755. MR 373300, DOI 10.1090/S0025-5718-1974-0373300-4
R. S. Varga, Functional analysis and approximation theory in numerical analysis, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 3, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. MR 0310504
Carl de Boor, On calculating with $B$-splines, J. Approximation Theory 6 (1972), 50–62. MR 338617, DOI 10.1016/0021-9045(72)90080-9