Editing Runge–Kutta methods (section)

==References==
* {{Citation | last1=Runge | first1=Carl David Tolmé | author1-link=Carl David Tolmé Runge | title=Über die numerische Auflösung von Differentialgleichungen | publisher=[[Springer Science+Business Media|Springer]] | journal=Mathematische Annalen | volume=46 | number=2 | pages=167–178 | year=1895 |doi=10.1007/BF01446807| s2cid=119924854 | url=https://zenodo.org/record/2178704 }}.
* {{Citation | last1=Kutta | first1=Wilhelm | title=Beitrag zur näherungsweisen Integration totaler Differentialgleichungen | journal=Zeitschrift für Mathematik und Physik | volume=46 | pages=435–453 | year=1901|url=https://archive.org/details/zeitschriftfrma12runggoog/page/434/}}.
* {{Citation | last1=Ascher | first1=Uri M. | last2=Petzold | first2=Linda R.|author2-link=Linda Petzold | title=Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations | publisher=[[Society for Industrial and Applied Mathematics]] | location=Philadelphia | isbn=978-0-89871-412-8 | year=1998}}.
* {{Citation | last1=Atkinson | first1=Kendall A. | title=An Introduction to Numerical Analysis | publisher=[[John Wiley & Sons]] | location=New York | edition=2nd | isbn=978-0-471-50023-0 | year=1989}}.
* {{Citation| last1 = Butcher | first1 = John C. | author1-link=John C. Butcher | title=Coefficients for the study of Runge-Kutta integration processes | journal = Journal of the Australian Mathematical Society | doi=10.1017/S1446788700027932 | volume=3 | issue=2 |date=May 1963 | pages=185–201| doi-access=free }}.
* {{Citation| last1 = Butcher | first1 = John C. | author1-link=John C. Butcher | title=On Runge-Kutta processes of high order| journal = Journal of the Australian Mathematical Society | doi=10.1017/S1446788700023387| volume=4 | issue=2 |date=May 1964 | pages=179–194| doi-access=free }}
* {{Citation | last1=Butcher | first1=John C. | author1-link=John C. Butcher | title= A stability property of implicit Runge-Kutta methods| year=1975 |journal= BIT| volume= 15 | issue=4 |pages= 358–361 | doi=10.1007/bf01931672| s2cid=120854166 }}.
* {{Citation | last1=Butcher | first1=John C. | author1-link=John C. Butcher | title= Numerical methods for ordinary differential equations in the 20th century| year=2000 |journal= J. Comput. Appl. Math.| volume= 125 | issue=1–2 |pages= 1–29 | doi=10.1016/S0377-0427(00)00455-6 | bibcode=2000JCoAM.125....1B | doi-access=free }}.
* {{Citation | last1=Butcher | first1=John C. | author1-link=John C. Butcher | title=Numerical Methods for Ordinary Differential Equations | publisher=[[John Wiley & Sons]] | location=New York | isbn=978-0-470-72335-7 | year=2008}}.
* {{Citation | last1=Cellier | first1=F. | last2=Kofman | first2=E. | title=Continuous System Simulation | publisher=[[Springer Verlag]] | isbn=0-387-26102-8 | year=2006}}.
* {{Citation | last1=Dahlquist | first1=Germund | author1-link=Germund Dahlquist | title=A special stability problem for linear multistep methods | doi=10.1007/BF01963532 | year=1963 | journal=BIT | issn=0006-3835 | volume=3 | pages=27–43| hdl=10338.dmlcz/103497 | s2cid=120241743 | hdl-access=free }}.
* {{Citation | last1=Forsythe | first1=George E. | last2=Malcolm | first2=Michael A. | last3=Moler | first3=Cleve B. | title=Computer Methods for Mathematical Computations | publisher=[[Prentice-Hall]] | year = 1977}} (see Chapter 6).
* {{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}.
* {{Citation | last1=Hairer | first1=Ernst | last2=Wanner | first2=Gerhard | title=Solving ordinary differential equations II: Stiff and differential-algebraic problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-3-540-60452-5 | year=1996}}.
* {{Citation | last1=Iserles | first1=Arieh | author1-link=Arieh Iserles | title=A First Course in the Numerical Analysis of Differential Equations | publisher=[[Cambridge University Press]] | isbn=978-0-521-55655-2 | year=1996| bibcode=1996fcna.book.....I }}.
* {{Citation|last1=Lambert|first1=J.D| title=Numerical Methods for Ordinary Differential Systems. The Initial Value Problem | publisher=[[John Wiley & Sons]]|year=1991 | isbn=0-471-92990-5}}
* {{Citation | last1=Kaw | first1=Autar | last2=Kalu | first2=Egwu | title=Numerical Methods with Applications | url=http://numericalmethods.eng.usf.edu/topics/textbook_index.html | publisher=autarkaw.com | edition=1st | year = 2008}}.
* {{Citation | last1=Press | first1=William H. | last2=Teukolsky | first2=Saul A. | author2-link=Saul Teukolsky | last3=Vetterling | first3=William T. | last4=Flannery | first4=Brian P. | title=Numerical Recipes: The Art of Scientific Computing | chapter=Section 17.1 Runge-Kutta Method | chapter-url=http://apps.nrbook.com/empanel/index.html#pg=907 | publisher=[[Cambridge University Press]] | edition=3rd | isbn=978-0-521-88068-8 | year=2007| title-link=Numerical Recipes }}. Also, [http://apps.nrbook.com/empanel/index.html#pg=910 Section 17.2. Adaptive Stepsize Control for Runge-Kutta].
* {{Citation | last1=Stoer | first1=Josef | last2=Bulirsch | first2=Roland | title=Introduction to Numerical Analysis | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=3rd | isbn=978-0-387-95452-3 | year=2002}}.
* {{Citation | last1=Süli | first1=Endre | last2=Mayers | first2=David | title=An Introduction to Numerical Analysis | publisher=[[Cambridge University Press]] | isbn=0-521-00794-1 | year=2003}}.
* {{Citation | last1=Tan | first1=Delin | last2=Chen | first2=Zheng | title=On A General Formula of Fourth Order Runge-Kutta Method | url=http://msme.us/2012-2-1.pdf | journal=Journal of Mathematical Science & Mathematics Education | volume=7 | issue=2 |pages = 1–10 |year = 2012}}.
* advance discrete maths ignou reference book (code- mcs033)
* John C. Butcher: "B-Series : Algebraic Analysis of Numerical Methods", Springer(SSCM, volume 55), {{ISBN|978-3030709556}} (April, 2021).
* {{Citation | last1=Butcher | first1=J.C. | title=The non-existence of ten stage eighth order explicit Runge-Kutta methods | url=https://link.springer.com/article/10.1007/BF01935372| journal=BIT Numerical Mathematics | volume=25 |pages = 521–540 |year = 1985| issue=3 | doi=10.1007/BF01935372 }}.
* {{Citation | last1=Butcher | first1=J.C. | title=On the attainable order of Runge-Kutta methods | url=https://www.ams.org/journals/mcom/1965-19-091/S0025-5718-1965-0179943-X/ | journal=Mathematics of Computation| volume=19 |pages = 408–417 |year = 1965| issue=91 | doi=10.1090/S0025-5718-1965-0179943-X }}.
* {{Citation | last1=Curtis | first1=A.R. | title=An eighth order Runge-Kutta process with eleven function evaluations per step | url=https://link.springer.com/article/10.1007/BF02219778 | journal=Numerische Mathematik| volume=16 |pages = 268–277 |year = 1970| issue=3 | doi=10.1007/BF02219778 }}.
* {{Citation | last1=Cooper | first1=G.J. | last2=Verner | first2=J.H. | title=Some Explicit Runge–Kutta Methods of High Order | url=https://epubs.siam.org/doi/abs/10.1137/0709037?journalCode=sjnaam | journal=SIAM Journal on Numerical Analysis| volume=9 | year = 1972| issue=3 | pages=389–405 | doi=10.1137/0709037 | bibcode=1972SJNA....9..389C }}.
* {{Citation | last1=Butcher | first1=J.C. | title=A History of Runge-Kutta Methods | url=https://dx.doi.org/10.1016/0168-9274%2895%2900108-5 | journal=Applied Numerical Mathematics | volume=20 | pages=247–260 | year = 1996| issue=3 | doi=10.1016/0168-9274(95)00108-5 }}.