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Why Implicit Runge Kutta is implicit? Moreover there is adaptive Runge Kutta, etc. All them them can solve IVP problem (implicit differential equation). What the real reason why this particular method is implicit?

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You surely refer with IVP to Initial Value Problems?

"Implicit" in general means that to get to the desired value you have to solve a , in general non-linear, system of equations instead of just evaluating a function, which would give you an explicit method to get at the desired value.