On implicit Runge–Kutta methods received as a result of inversion of explicit methods

Inverse methods for explicit Runge–Kutta methods are considered. Such methods have a number of advantages, but their drawback is the low (1st) stage order. It leads to reduction of real order when solving stiff and differential-algebraic equations. The new methods possessing properties of methods of higher stage order are offered. Results of numerical experiments show that the offered methods allow us to avoid an order reduction.