Elliptic spline functions and the Rayleigh-Ritz-Galerkin method
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- by Martin H. Schultz PDF
- Math. Comp. 24 (1970), 65-80 Request permission
Abstract:
Error estimates for the Rayleigh-Ritz-Galerkin method, using finite-dimensional spline type spaces, for a class of nonlinear two-point boundary value problems are discussed. The results of this paper extend and improve recent corresponding results of B. L. Hulme, F. M. Perrin, H. S. Price, and R. S. Varga.References
- J. H. Ahlberg and E. N. Nilson, The approximation of linear functionals, SIAM J. Numer. Anal. 3 (1966), 173–182. MR 217500, DOI 10.1137/0703013
- G. Birkhoff, M. H. Schultz, and R. S. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations, Numer. Math. 11 (1968), 232–256. MR 226817, DOI 10.1007/BF02161845
- P. G. Ciarlet, M. H. Schultz, and R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem, Numer. Math. 9 (1966/67), 394–430. MR 221761, DOI 10.1007/BF02162155
- P. G. Ciarlet, M. H. Schultz, and R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. V. Monotone operator theory, Numer. Math. 13 (1969), 51–77. MR 250496, DOI 10.1007/BF02165273
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- Bernie L. Hulme, Interpolation by Ritz approximation, J. Math. Mech. 18 (1968/1969), 337–341. MR 0231537, DOI 10.1512/iumj.1969.18.18026
- G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR 0213785
- F. M. Perrin, H. S. Price, and R. S. Varga, On higher-order numerical methods for nonlinear two-point boundary value problems, Numer. Math. 13 (1969), 180–198. MR 255069, DOI 10.1007/BF02163236
- Milton E. Rose, Finite difference schemes for differential equations, Math. Comp. 18 (1964), 179–195. MR 183123, DOI 10.1090/S0025-5718-1964-0183123-0
- Martin H. Schultz, Error bounds for polynomial spline interpolation, Math. Comp. 24 (1970), 507–515. MR 275025, DOI 10.1090/S0025-5718-1970-0275025-9
- M. H. Schultz and R. S. Varga, $L$-splines, Numer. Math. 10 (1967), 345–369. MR 225068, DOI 10.1007/BF02162033
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 65-80
- MSC: Primary 65.62; Secondary 41.00
- DOI: https://doi.org/10.1090/S0025-5718-1970-0264857-9
- MathSciNet review: 0264857