Runge–Kutta methods (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Runge–Kutta methods" in English language version.

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ams.org (Global: 451^st place; English: 277^th place)

Butcher 1965, p. 408 Butcher, J.C. (1965), "On the attainable order of Runge-Kutta methods", Mathematics of Computation, 19 (91): 408–417, doi:10.1090/S0025-5718-1965-0179943-X.

archive.org (Global: 6^th place; English: 6^th place)

Hairer, Nørsett & Wanner (1993, p. 138) refer to Kutta (1901). Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York: Springer-Verlag, ISBN 978-3-540-56670-0. Kutta, Wilhelm (1901), "Beitrag zur näherungsweisen Integration totaler Differentialgleichungen", Zeitschrift für Mathematik und Physik, 46: 435–453.

dictionary.com (Global: 794^th place; English: 588^th place)

"Runge-Kutta method". Dictionary.com. Retrieved 4 April 2021.

doi.org (Global: 2^nd place; English: 2^nd place)

doi.org

Butcher 1965, p. 408 Butcher, J.C. (1965), "On the attainable order of Runge-Kutta methods", Mathematics of Computation, 19 (91): 408–417, doi:10.1090/S0025-5718-1965-0179943-X.
Butcher 1985 Butcher, J.C. (1985), "The non-existence of ten stage eighth order explicit Runge-Kutta methods", BIT Numerical Mathematics, 25 (3): 521–540, doi:10.1007/BF01935372.
Butcher 1964 Butcher, John C. (May 1964), "On Runge-Kutta processes of high order", Journal of the Australian Mathematical Society, 4 (2): 179–194, doi:10.1017/S1446788700023387
Curtis 1970, p. 268 Curtis, A.R. (1970), "An eighth order Runge-Kutta process with eleven function evaluations per step", Numerische Mathematik, 16 (3): 268–277, doi:10.1007/BF02219778.
Butcher 1996, p. 247 Butcher, J.C. (1996), "A History of Runge-Kutta Methods", Applied Numerical Mathematics, 20 (3): 247–260, doi:10.1016/0168-9274(95)00108-5.
This result is due to Dahlquist (1963). Dahlquist, Germund (1963), "A special stability problem for linear multistep methods", BIT, 3: 27–43, doi:10.1007/BF01963532, hdl:10338.dmlcz/103497, ISSN 0006-3835, S2CID 120241743.
Dormand, J. R.; Prince, P. J. (October 1978). "New Runge–Kutta Algorithms for Numerical Simulation in Dynamical Astronomy". Celestial Mechanics. 18 (3): 223–232. Bibcode:1978CeMec..18..223D. doi:10.1007/BF01230162. S2CID 120974351.
Qin, Meng-Zhao; Zhu, Wen-Jie (1991-01-01). "Canonical Runge-Kutta-Nyström (RKN) methods for second order ordinary differential equations". Computers & Mathematics with Applications. 22 (9): 85–95. doi:10.1016/0898-1221(91)90209-M. ISSN 0898-1221.

dx.doi.org

Butcher 1996, p. 247 Butcher, J.C. (1996), "A History of Runge-Kutta Methods", Applied Numerical Mathematics, 20 (3): 247–260, doi:10.1016/0168-9274(95)00108-5.
Qin, Meng-Zhao; Zhu, Wen-Jie (1991-01-01). "Canonical Runge-Kutta-Nyström (RKN) methods for second order ordinary differential equations". Computers & Mathematics with Applications. 22 (9): 85–95. doi:10.1016/0898-1221(91)90209-M. ISSN 0898-1221.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

This result is due to Dahlquist (1963). Dahlquist, Germund (1963), "A special stability problem for linear multistep methods", BIT, 3: 27–43, doi:10.1007/BF01963532, hdl:10338.dmlcz/103497, ISSN 0006-3835, S2CID 120241743.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Atkinson (1989, p. 423), Hairer, Nørsett & Wanner (1993, p. 134), Kaw & Kalu (2008, §8.4) and Stoer & Bulirsch (2002, p. 476) leave out the factor h in the definition of the stages. Ascher & Petzold (1998, p. 81), Butcher (2008, p. 93) and Iserles (1996, p. 38) use the y values as stages. Atkinson, Kendall A. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons, ISBN 978-0-471-50023-0. Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York: Springer-Verlag, ISBN 978-3-540-56670-0. Kaw, Autar; Kalu, Egwu (2008), Numerical Methods with Applications (1st ed.), autarkaw.com. Stoer, Josef; Bulirsch, Roland (2002), Introduction to Numerical Analysis (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-95452-3. Ascher, Uri M.; Petzold, Linda R. (1998), Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-412-8. Butcher, John C. (2008), Numerical Methods for Ordinary Differential Equations, New York: John Wiley & Sons, ISBN 978-0-470-72335-7. Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 38 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 39 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 41; Süli & Mayers 2003, pp. 351–352 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2. Süli, Endre; Mayers, David (2003), An Introduction to Numerical Analysis, Cambridge University Press, ISBN 0-521-00794-1.
Iserles 1996, pp. 43–44 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 47 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 60 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, pp. 62–63 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Iserles 1996, p. 63 Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.
Dormand, J. R.; Prince, P. J. (October 1978). "New Runge–Kutta Algorithms for Numerical Simulation in Dynamical Astronomy". Celestial Mechanics. 18 (3): 223–232. Bibcode:1978CeMec..18..223D. doi:10.1007/BF01230162. S2CID 120974351.

ncu.edu.tw (Global: low place; English: low place)

ss.ncu.edu.tw

Lyu, Ling-Hsiao (August 2016). "Appendix C. Derivation of the Numerical Integration Formulae" (PDF). Numerical Simulation of Space Plasmas (I) Lecture Notes. Institute of Space Science, National Central University. Retrieved 17 April 2022.

nrbook.com (Global: low place; English: low place)

apps.nrbook.com

Press et al. 2007, p. 908; Süli & Mayers 2003, p. 328 Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007), "Section 17.1 Runge-Kutta Method", Numerical Recipes: The Art of Scientific Computing (3rd ed.), Cambridge University Press, ISBN 978-0-521-88068-8. Also, Section 17.2. Adaptive Stepsize Control for Runge-Kutta. Süli, Endre; Mayers, David (2003), An Introduction to Numerical Analysis, Cambridge University Press, ISBN 0-521-00794-1.
Press et al. 2007, p. 907 Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007), "Section 17.1 Runge-Kutta Method", Numerical Recipes: The Art of Scientific Computing (3rd ed.), Cambridge University Press, ISBN 978-0-521-88068-8. Also, Section 17.2. Adaptive Stepsize Control for Runge-Kutta.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

This result is due to Dahlquist (1963). Dahlquist, Germund (1963), "A special stability problem for linear multistep methods", BIT, 3: 27–43, doi:10.1007/BF01963532, hdl:10338.dmlcz/103497, ISSN 0006-3835, S2CID 120241743.
Dormand, J. R.; Prince, P. J. (October 1978). "New Runge–Kutta Algorithms for Numerical Simulation in Dynamical Astronomy". Celestial Mechanics. 18 (3): 223–232. Bibcode:1978CeMec..18..223D. doi:10.1007/BF01230162. S2CID 120974351.

springer.com (Global: 274^th place; English: 309^th place)

link.springer.com

Butcher 1985 Butcher, J.C. (1985), "The non-existence of ten stage eighth order explicit Runge-Kutta methods", BIT Numerical Mathematics, 25 (3): 521–540, doi:10.1007/BF01935372.
Curtis 1970, p. 268 Curtis, A.R. (1970), "An eighth order Runge-Kutta process with eleven function evaluations per step", Numerische Mathematik, 16 (3): 268–277, doi:10.1007/BF02219778.

usf.edu (Global: 3,436^th place; English: 2,114^th place)

numericalmethods.eng.usf.edu

Atkinson (1989, p. 423), Hairer, Nørsett & Wanner (1993, p. 134), Kaw & Kalu (2008, §8.4) and Stoer & Bulirsch (2002, p. 476) leave out the factor h in the definition of the stages. Ascher & Petzold (1998, p. 81), Butcher (2008, p. 93) and Iserles (1996, p. 38) use the y values as stages. Atkinson, Kendall A. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons, ISBN 978-0-471-50023-0. Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York: Springer-Verlag, ISBN 978-3-540-56670-0. Kaw, Autar; Kalu, Egwu (2008), Numerical Methods with Applications (1st ed.), autarkaw.com. Stoer, Josef; Bulirsch, Roland (2002), Introduction to Numerical Analysis (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-95452-3. Ascher, Uri M.; Petzold, Linda R. (1998), Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-412-8. Butcher, John C. (2008), Numerical Methods for Ordinary Differential Equations, New York: John Wiley & Sons, ISBN 978-0-470-72335-7. Iserles, Arieh (1996), A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Bibcode:1996fcna.book.....I, ISBN 978-0-521-55655-2.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

This result is due to Dahlquist (1963). Dahlquist, Germund (1963), "A special stability problem for linear multistep methods", BIT, 3: 27–43, doi:10.1007/BF01963532, hdl:10338.dmlcz/103497, ISSN 0006-3835, S2CID 120241743.
Qin, Meng-Zhao; Zhu, Wen-Jie (1991-01-01). "Canonical Runge-Kutta-Nyström (RKN) methods for second order ordinary differential equations". Computers & Mathematics with Applications. 22 (9): 85–95. doi:10.1016/0898-1221(91)90209-M. ISSN 0898-1221.

Runge–Kutta methods (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

archive.org (Global: 6th place; English: 6th place)

dictionary.com (Global: 794th place; English: 588th place)

doi.org (Global: 2nd place; English: 2nd place)