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Symmetric Runge-Kutta methods with higher derivatives and quadratic extrapolation

Kulikov, Gennady Yu; Khrustaleva, E.Yu.; Merkulov, A.I.

Lecture Notes in Computer Science, 3991 (2006), 117-123

In this paper we study the symmetry of Runge-Kutta methods with higher derivatives. We find conditions which provide this property for the above numerical methods. We prove that the family of E-methods constructed earlier consists of symmetric methods only, which lead to the quadratic extrapolation technique in practice.