Abstract
Recently, Chawla and Al-Zanaidi [7] examined stability of the class of extended one-step methods introduced in [6] for the numerical integration of first-order initial value problems y′ = f(t y); y(t 0) = n which possess oscillating solutions. They obtained non-dissipative methods of orders two to five, while the maximum possible order of an extended one-step method is seven [10]. In the present paper we investigate the existence of non-dissipative extended one-step methods of orders six and seven. We show that there exists a uniquely determined non-dissipative method of order six. We derive a two-parameter family of extended one-step methods of order seven; while there exists no non-dissipative method, we obtain a method of order seven which is “almost” non-dissipative. The present methods are computationally tested by an example.
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