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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.

MSC:
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
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