Abstract: Two finite difference three-level alternating methods for the two-dimensional heat equation on a structured triangular mesh are obtained numerically. They are ABd( Alternating Band) and ABdE-I(Ahernating Band Explicit-Implicit) methods. An alternating technique using different schemes in neighboring time levels and spatial domain is employed. A theoretical analysis and numerical experiments demonstrate that both methods show obvious parallelism, good accuracy and unconditional stability.

Key words: parabolic equation, finite difference, structured triangular mesh, three-level alternating method