A STABLE ALGORITHM FOR SOLVING A 2D 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. 2533.
For a 1D case, a regionbyregion algorithm is developed which approximates the conjugate conditions with 0(h^{2} + τ) order. For some limiting cases, the unconditional algorithm stability is investigated and analytically proved. The algorithm is generalyzed to a 2D case where the heat conduction equation is approximated with a nodetype scheme. The numerical results indicate that the algorithm yields a high actual accuracy and unconditional stability for a 2D heat conduction equation solved by regions on substantially nonorthogonal and nonuniform meshes with sufficiently large time steps.
