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van der Houwen, P. J.; Sommeijer, B. P.

On the internal stability of explicit, m-stage Runge-Kutta methods for large m-values. (English) Zbl 0455.65052

Z. Angew. Math. Mech. 60, 479-485 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 2 Reviews
Cited in 91 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65N40 Method of lines for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

internal stability; explicit, m-stage Runge-Kutta methods
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References:

[1] Frank, J. Assoc. Comput. Machin. 7 pp 274– (1960) · Zbl 0097.11404 · doi:10.1145/321033.321041
[2] Gentsch, ZAMM 58 pp t415– (1978)
[3] Construction of Integration Formulas for Initial Value Problems, North-Holland Publ. Comp., Amsterdam 1977.
[4] Computational Methods in Ordinary Differential Equations, John Wiley & Sons, London 1973.
[5] Verwer, J. Comput. Appl. Math. 3 pp 155– (1977)
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