Computing eigenvalues of ordinary differential equations by finite differences
HTML articles powered by AMS MathViewer
- by John Gary PDF
- Math. Comp. 19 (1965), 365-379 Request permission
References
- R. Courant, K. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), no. 1, 32–74 (German). MR 1512478, DOI 10.1007/BF01448839
- H. F. Weinberger, Lower bounds for higher eigenvalues by finite difference methods, Pacific J. Math. 8 (1958), 339–368; erratum, 941. MR 107372
- George E. Forsythe, Asymptotic lower bounds for the fundamental frequency of convex membranes, Pacific J. Math. 5 (1955), 691–702. MR 73048
- Beresford Parlett, Laguerre’s method applied to the matrix eigenvalue problem, Math. Comp. 18 (1964), 464–485. MR 165668, DOI 10.1090/S0025-5718-1964-0165668-2
- David E. Muller, A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comput. 10 (1956), 208–215. MR 83822, DOI 10.1090/S0025-5718-1956-0083822-0
- Werner L. Frank, Finding zeros of arbitrary functions, J. Assoc. Comput. Mach. 5 (1958), 154–160. MR 144457, DOI 10.1145/320924.320928
- E. Bodewig, Sur la méthode de Laguerre pour l’approximation des racines de certaines équations algébriques et sur la critique d’Hermite, Nederl. Akad. Wetensch., Proc. 49 (1946), 911–921 = Indagationes Math. 8, 570–580 (1946) (French). MR 25809
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Francis D. Murnaghan, The calculus of variations, Lectures on Applied Mathematics, Vol. 2, Spartan Books, Washington, D.C., 1962. MR 0222733
- L. Fox, The numerical solution of two-point boundary problems in ordinary differential equations, Oxford University Press, New York, 1957. MR 0102178
- R. W. Hamming, Numerical methods for scientists and engineers, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York-San Francisco, Calif.-Toronto-London, 1962. MR 0137279
- George E. Forsythe and Wolfgang R. Wasow, Finite-difference methods for partial differential equations, Applied Mathematics Series, John Wiley & Sons, Inc., New York-London, 1960. MR 0130124
- John H. Giese, On the truncation error in a numerical solution of the Neumann problem for a rectangle, J. Math. and Phys. 37 (1958), 169–177. MR 96361, DOI 10.1002/sapm1958371169 J. Green, “A problem in baroclinic stability,” Quart. J. Royal Meteorological Soc., v. 86, 1960, pp. 237–252.
- Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
- Edward F. Kurtz Jr. and Stephen H. Crandall, Computer-aided analysis of hydrodynamic stability, J. Math. and Phys. 41 (1962), 264–279. MR 143420
Additional Information
- © Copyright 1965 American Mathematical Society
- Journal: Math. Comp. 19 (1965), 365-379
- MSC: Primary 65.62; Secondary 65.40
- DOI: https://doi.org/10.1090/S0025-5718-1965-0179926-X
- MathSciNet review: 0179926