Solving linear boundary value problems by approximating the coefficients
HTML articles powered by AMS MathViewer
- by Steven A. Pruess PDF
- Math. Comp. 27 (1973), 551-561 Request permission
Abstract:
A method for solving linear boundary value problems is described which consists of approximating the coefficients of the differential operator. Error estimates for the approximate solutions are established and improved results are given for the case of approximation by piecewise polynomial functions. For the latter approximations, the resulting problem can be solved by Taylor series techniques and several examples of this are given.References
-
M. Alexander & R. Gordon, "A new method for constructing solutions to time dependent perturbation equations," J. Chem. Phys., v. 55, 1971, pp. 4889-4898.
J. Canosa & R. Gomes de Oliveira, "A new method for the solution of the Schrödinger equation," J. Comput. Phys., v. 5, 1970, pp. 188-207.
- Randal H. Cole, Theory of ordinary differential equations, Appleton-Century-Crofts [Meredith Corporation], New York, 1968. MR 0239155
- Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604 R. Gordon, "Quantum scattering using piecewise analytic solutions," in Computational Physics. Vol. 10 (Edited by B. Adler), Academic Press, New York, 1971, pp. 81-109.
- Herbert B. Keller, Numerical methods for two-point boundary-value problems, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0230476 J. Nécas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris; Academia, Prague, 1967. MR 37 #3168.
- Steven Pruess, Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation, SIAM J. Numer. Anal. 10 (1973), 55–68. MR 327048, DOI 10.1137/0710008 A. Roark & L. Shampine, On the Numerical Solution of a Linear Two-Point Boundary Value Problem, Sandia Laboratory Technical Memorandum SC-TM-67-588, September 1967.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 551-561
- MSC: Primary 65N15
- DOI: https://doi.org/10.1090/S0025-5718-1973-0371100-1
- MathSciNet review: 0371100