Introduction to B-series

References

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[J.C. Butcher, 1964],

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[J.C. Butcher, 1966],

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[J.C. Butcher, 1969)],

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[J.C. Butcher, 1972],

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[J.C. Butcher, 1987],

The numerical analysis of ordinary differential equations, Wiley, Chichester, 512 pages.

[J.C. Butcher, 2008],

Numerical methods for ordinary differential equations, second edition, John Wiley & Sons Ltd., Chichester, 463 pages.

[J.C. Butcher, 2021],

B-Series: An algebraic analysis of numerical methods, Springer–Verlag, 310 pages.

[E. Hairer, 1978],

A Runge–Kutta method of order 10, J. Inst. Maths. Applics., 21, 47–59.

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Butcher,J.C.: B-series: Algebraic Analysis of Numerical Methods, Springer-Verlag (2021)

Hairer,~E. and Wanner,~G.: \textcolor{blue}{\sl\bfseries Multistep-multistage-\\multiderivative methods for ordinary differential equations,} Computing {\bf 11}, 287--303 (1973)

Hairer,~E. and Wanner,~G.: \textcolor{blue}{\sl\bfseries On the Butcher group and general multi-value methods,} Computing {\bf 13}, 1--15 (1974)

[W. Kutta, 1901],

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[C. Runge, 1895],

Über die numerische Auflösung von Differentialgleichungen, Math. Ann., 46, 167–178.

$\to$ The first sixth order methods