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2.2.4 The Codes RKSUITE

RKSUITE is an excellent collection of codes based on Runge-Kutta methods for the numerical solution of an IVP for a first order system of ODEs and is available in the public domain. It supersedes some very widely used codes written by the authors and their coauthors, namely the RKF45 code and its descendant DDERKF in the SLATEC library and DO2PAF and associated codes in the NAG Fortran library. RKSUITE is written in standard FORTRAN 77 and is distributed in source form. The advanced algorithms provide more functionality than is found in earlier codes, including new more efficient formulas, interpolation, automatic selection of the initial step size, a stiffness diagnostic, and global error assessment. The advanced software design includes a novel interface permitting both interval- and step-oriented solutions and is highly portable. The documentation includes detailed instructions for the effective use of the codes, a collection of templates illustrating the use of the codes for common tasks, output from running the templates in a number of variations, and comprehensive instructions for installing the codes.

RKSUITE implements three Runge-Kutta pairs: (2,3), (4,5), and (7,8). The (4,5) pair, for example, uses both a 4th and a 5th order approximation to estimate the error in the 4th order formula; using extrapolation, it then produces a formula of order 5. Similarly, the (2,3) pair produces a formula of order 3 and the (7,8) pair a formula of order 8.