An investigation of Runge-Kutta processes, and equivalence of scalar and vector cases
type: Item
instance of: scholarly article
title: An investigation of Runge-Kutta processes, and equivalence of scalar and vector cases
zbMATH Open document ID: 0552.65057
DOI: 10.1016/0022-247X(84)90021-0
author: Diran Sarafyan
author: Curtis Outlaw
author: Leroy Derr
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The application of Runge-Kutta methods of order m for systems: \(y'=f(x,y)\), \(y(x_ 0)=y_ 0\), generates a system of nonlinear algebraic equations whose number increases rapidly with m (reaching for \(m=14\), 3259 equations for the scalar case, 53272 for the vector case). The authors show how these numbers may be obtained for any m by counting certain types of tree graphs which correspond to the expression in the form of a tensor structure of the differential operators that appear in the process. They also give for fifth- and sixth-order formulae criteria under which both scalar and vector systems reduce to the same equivalent system. Some errors in previous concerning papers are indicated.
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 3880025
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: systems
zbMATH Keywords: sixth-order formulae
reviewed by: Antonio de Castro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3880025