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Some New RKT‐Formulas for First‐Order Differential Equations Requiring a Minimum Number of Differentiations
Author(s) -
Fehlberg E.
Publication year - 1980
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19800600403
Subject(s) - mathematics , quadrature (astronomy) , differential equation , fraction (chemistry) , order (exchange) , calculus (dental) , mathematical analysis , physics , finance , optics , economics , medicine , chemistry , organic chemistry , dentistry
For first‐order differential equations, new RKT (Runge‐Kutta‐Transformation)‐formulas with stepsize control are derived. Formulas of the 9th, 11th, and 13 th order are presented requiring a minimum number of differentiations of the differential equations. Their coefficients are tabulated in fraction form. The application of the formulas to quadrature problems is discussed in an appendix.