In this paper, a new definition on harmonious dissipative operators is given and some important properties of theirs are shown. Especially, the relationship between a harmonious dissipative operator and the completely square conservative difference scheme in an explicit way is revealed. Kinds of 2-order, 3-order and 4-order harmonious dissipative operators are constructed by using the traditional Runge-Kutta method and a species of general m-order harmonious dissipative operators is established in the linear case. In addition, an efficiency parameter to appraise the time benefits of a harmonious dissipative operator is defined in this paper. It is testified in numerical tests that the harmonious dissipative operators are indeed able to improve the time-efficiency and computational effect of the completely square conservative difference scheme in an explicit way.
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