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A STABLE ALGORITHM FOR SOLVING A 2-D HEAT CONDUCTION EQUATION BY REGION USING A NODE DIFFERENCE SCHEME

R. M. Shagaliev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1984. Вып.3. С. 25-33.

      For a 1-D case, a region-by-region algorithm is developed which approximates the conjugate conditions with 0(h2 + τ) order. For some limiting cases, the unconditional algorithm stability is investigated and analytically proved. The algorithm is generalyzed to a 2-D case where the heat conduction equation is approximated with a node-type scheme. The numerical results indicate that the algorithm yields a high actual accuracy and unconditional stability for a 2-D heat conduction equation solved by regions on substantially nonorthogonal and nonuniform meshes with sufficiently large time steps.










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