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RungeKuttaOrderConditions

RungeKuttaOrderConditions[p, s]
gives a list of the order conditions that any s-stage Runge-Kutta method of order p must satisfy.
RungeKuttaOrderConditions[p]
gives the order conditions using stage-independent tensor notation.
  • The order conditions are grouped by order.
  • The following options can be given:
ButcherRowSumFalsewhether to include row-sum conditions for c_(i)
ButcherSimplifyFalsewhether to use Butcher's assumptions
ContinuousExtension$ContinuousExtensionwhether to generate conditions for continuous extensions
RungeKuttaMethod$RungeKuttaMethodtype of Runge-Kutta method
  • If the option ButcherSimplify->True is selected, the number of stages must be a positive integer.