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On a family of A-stable collocation methods with high derivatives

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

Lecture Notes in Computer Science, 3037 (2004), 73-80

In this paper we develop a family of A-stable one-step methods with high derivatives by means of a collocation technique. We present construction details and a theory to justify such sort of methods. We also concentrate on an effective way of their practical implementation.