A class of two_level explicit difference schemes are presented for solving three_dimensional heat conduction equation. When the order of truncation error is O( Δ t+( Δ x) 2), the stability condition is mesh ratio r= Δ t( Δ x) 2= Δ t( Δ y) 2= Δ t( Δ z) 2≤12, which is better than that of all the other explicit difference schemes. And when the order of truncation error is O(( Δ t) 2+( Δ x) 4), the stability condition is r≤1/6, which contains the known results.
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