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Adomian decomposition method for three-dimensional parabolic equation with non-classic boundary conditions. (English) Zbl 1132.35385
Summary: Adomian decomposition method is developed for solving an initial-boundary value problem for the three-dimensional parabolic partial differential equation with non-classical boundary conditions. The approximate solutions of this problem are calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with analytical, approximate and numerieal results [M. Dehghan, Appl. Math. Comput. 137, No. 2–3, 399–412 (2003; Zbl 1027.65127)]. The results show that the present method is more accurate than other numerical methods. We will be obtaining exact solutions without using any transformation.

35K05 Heat equation
35A35 Theoretical approximation in context of PDEs
35A25 Other special methods applied to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations