Publication record · 18.cifr/1980.dormand.rkf45
18.cifr/1980.dormand.rkf45A family of embedded Runge-Kutta formulae is derived. These formulae minimize the local truncation error of the higher order formula so that the higher order formula can be used for propagation. Conventional Runge-Kutta-Fehlberg methods use the lower order formula for propagation. Numerical results show a marked improvement in efficiency and accuracy over methods of similar order.
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The authors suggest extending the approach to higher-order pairs (7-8). Stiff systems are not addressed and implicit/SDIRK analogs remain an open extension. Dense output (continuous interpolation) was later developed as a follow-up but is not in the original paper.