Coefficients for the study of Runge-Kutta integration processes

1963/05/01 by J. C. Butcher · 9 citations
Mathematics · #Applied mathematics #Computer science #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Differential equation #Mathematical analysis #Mathematics #Numerical methods for differential equations #Order (exchange) #Pure mathematics #Runge–Kutta methods #Set (abstract data type) #Statistics #Variable (mathematics) #Variables

paper · pdf · doi:10.1017/s1446788700027932

crossref issued 1963/05/01 · crossref published 1963/05/01 · crossref published-print 1963/05/01 · openalex publication_date 1963/05/01 · crossref published-online 2009/04/09 · crossref created 2009/04/14 · crossref deposited 2019/06/04 · openalex created_date 2025/10/10 · crossref indexed 2026/08/02 · openalex updated_date 2026/08/04

Abstract

We consider a set of η first order simultaneous differential equations in the dependent variables y 1 , y 2 , …, y n and the independent variable x ⋮ No loss of gernerality results from taking the functions f 1 , f 2 , …, f n to be independent of x , for if this were not so an additional dependent variable y n+1 , anc be introduced which always equals x and thus satisfies the differential equation

Citations

• A process for the step-by-step integration of differential equations in an automatic digital computing machine

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