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Solution of a parabolic equation with a time-dependent coefficient and an extra measurement using the decomposition procedure of Adomian. (English) Zbl 1102.65127

This paper deals with resolution of partial differential equation by means of the Adomian decomposition method. This technique gives an analytical solution and does not need any discretization or linearization. The authors consider a linear heat equation where an unknown parameter has to be identified. Initial and boundary conditions are associated. But a difficulty is not solved in this paper. The boundary conditions are not taken into account in the resolution. Only the initial condition is considered. The consequence is that the solution obtained by the Adomian method does not depend on the two boundary conditions \(g_0(t)\) and \(g_1(t)\)!! Consequently, the authors must explain why they obtain a correct solution for the two examples considered in this paper.
A difficulty of the Adomian method is to take into account initial and boundary conditions in the canonical form. The two authors have to think about that before solving partial differential equations.

MSC:

65N99 Numerical methods for partial differential equations, boundary value problems
35F30 Boundary value problems for nonlinear first-order PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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