×

zbMATH — the first resource for mathematics

Rational approximations of trigonometric matrices with application to second-order systems of differential equations. (English) Zbl 0408.65047

MSC:
65L05 Numerical methods for initial value problems
41A21 Padé approximation
68Q25 Analysis of algorithms and problem complexity
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bathe, K.; Wilson, E., Numerical methods in finite element analysis, (1976), Prentice-Hall Englewood Cliffs, NJ
[2] Birkhoff, G.; Varga, R.S., Discretization errors for well-set Cauchy problems I, J. math. and phys., 44, 1-23, (1965) · Zbl 0134.13406
[3] J. H. Bramble and G. A. Baker, The construction and analysis of high order single step Galerkin approximations for initial boundary value problems for parabolic equations, to appear.
[4] Baker, G.A.; Bramble, J.H.; Thomée, V., Single step methods for parabolic problems, Math. comp., 31, 818-847, (1977) · Zbl 0378.65061
[5] Cavendish, J.C.; Culham, W.E.; Varga, R.S., A comparison of Crank-Nicolson and Chebyshev rational methods for numerically solving linear parabolic equations, J. comp. phys., 10, 354-368, (1972) · Zbl 0263.65090
[6] Cody, W.J.; Meinardus, G.; Varga, R.S., Chebyshev rational approximations to e-x in [0, +∞) and applications to heat-conduction problems, J. approximation theory, 2, 50-65, (1969) · Zbl 0187.11602
[7] Dougalis, V.A., High order fully discrete Galerkin approximations to hyperbolic equations, Ph.D. thesis, (1976), Harvard Univ
[8] Ehle, B.L., A-stable methods and Padé approximation to the exponential, SIAM J. math. anal, 4, 671-680, (1973) · Zbl 0236.65016
[9] Ehle, B.L.; Picel, Z., Two-parameter arbitrary order exponential approximations for stiff equations, Math. comp, 29, 501-511, (1975) · Zbl 0302.65059
[10] Fujii, H., Finite element schemes: stability and convergence, (), 201-218
[11] Gear, C.W., Numerical initial value problems in ordinary differential equations, (1971), Prentice-Hall Englewood Cliffs, N.J · Zbl 0217.21701
[12] Henrici, P., Discrete variable methods in ordinary differential equations, (1962), Wiley New York · Zbl 0112.34901
[13] Kreig, R.D.; Key, S.W., Transient shell response by numerical time integration, (), 237-258
[14] Lambert, J.D., Computational methods in ordinary differential equations, (1973), Wiley New York · Zbl 0258.65069
[15] Liniger, W.; Willoughby, R.A., Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. num. anal., 7, 47-65, (1970) · Zbl 0187.11003
[16] Morino, L.; Leech, J.W.; Witmer, E., Optimal predictor-corrector methods for systems of second-order differential equations, Aiia j., 12, 1343-1347, (1974) · Zbl 0295.65046
[17] Newmark, N.M., A method of computation for structural dynamics, Proc. amer. soc. civ. engrs., 85, 67-94, (1959)
[18] Norsett, S.P., One-step methods of Hermite type for numerical integration of stiff systems, Bit, 4, 63-77, (1974) · Zbl 0278.65078
[19] Norsett, S.P., C-polynomials for rational approximations to the exponential function, Num. math., 25, 39-56, (1975) · Zbl 0299.65010
[20] Ralston, R., A first course in numerical analysis, (1965), McGraw-Hill New York · Zbl 0139.31603
[21] Richtmyer, R.D.; Morton, K.W., Difference methods for initial-value problems, (1967), Interscience · Zbl 0155.47502
[22] Varga, R.S., On higher order stable implicit methods for solving parabolic partial differential equations, J. math and phys., 40, 220-231, (1961) · Zbl 0106.10805
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.