×

Block methods for second order ODEs. (English) Zbl 0744.65045

Author’s summary: Zero-stable block methods of orders 3/4 are proposed for second-order initial value problems \(y''=f(x,y)\), \(y(0)\), \(y'(0)\) given. The matrix coefficients of the schemes are chosen as to ensure zero-stability and consistency. There is anticipated speed up of computations as a result of admissible parallelism across the method and cheap error estimators.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1109/TC.1987.1676902
[2] DOI: 10.1137/0908039 · Zbl 0628.65054
[3] DOI: 10.1007/BF01931689 · Zbl 0378.65043
[4] DOI: 10.1137/1027140 · Zbl 0602.65047
[5] DOI: 10.1137/0708018 · Zbl 0216.48901
[6] Duff, I.S. 1987.The influence of vector and parallel processors on Numerical Analysis State of the Art in Numerical Analysis II, Edited by: Iserles, A. and Powell, M.J.D. 359–407. Oxford: Clarendon Press.
[7] Fatunla S.O., Numerical Initial Value Problems in Ordinary Differential Equations (1988) · Zbl 0651.65054
[8] DOI: 10.1109/TC.1978.1675121 · Zbl 0379.68033
[9] Gear, C.W. 1987a.The potential for parallelism in ODEs Computational Mathematics J, Edited by: Fatunla, S.O. 33–48. Dublin, Ireland: Boole Press.
[10] Gear C.W., Department of Computer Science (1987)
[11] DOI: 10.1007/BF01401041 · Zbl 0393.65035
[12] Henrici P., Discrete variable methods for ODEs (1962) · Zbl 0112.34901
[13] Iserles A., Technical Report (1988)
[14] Jakson K., Part I, R-K-F in standard form Tech. Rep (1988)
[15] Jeltsch R., yn = f(x,y), Math. Comp 32 pp 1108– (1978)
[16] DOI: 10.1093/imamat/18.2.189 · Zbl 0359.65060
[17] Milne W.E., Numerical solution of Differential equations (1953) · Zbl 0050.12202
[18] DOI: 10.1090/S0025-5718-1967-0223106-8
[19] Moulton F.R., New Methods in exterior ballistics (1926) · JFM 52.0806.04
[20] Nievergelt J., Comm. ACM 9 pp 417– (1964)
[21] Ortega J.M., SI AM Review 27 pp 413– (1985) · Zbl 0644.65075
[22] DOI: 10.1137/1009069 · Zbl 0243.65041
[23] DOI: 10.1090/S0025-5718-1969-0264854-5
[24] Skeel R.D., Center for supercomputing research and development (1987)
[25] DOI: 10.1093/imanum/7.4.407 · Zbl 0631.65074
[26] DOI: 10.1007/BF01932819 · Zbl 0253.65045
[27] DOI: 10.1109/TC.1976.1674545 · Zbl 0359.65063
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.