## Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications.(English)Zbl 1054.65105

Summary: We are concerned with the solution of a nonlocal boundary value problem. An approach is presented for solving the two-dimensional parabolic partial differential equation subject to integral boundary specifications. The main objective is to propose an alternative method of solution, one not based on finite difference methods or finite element schemes or spectral techniques.
The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the two-dimensional linear parabolic partial differential equation with nonlocal boundary specifications replacing the classical boundary conditions. The Adomian decomposition method is used by many researchers to investigate several scientific applications and requires less work if compare with the traditional techniques. The introduction of this idea as will be discussed, not only provides the solution in a series form but it also guarantees considerable saving of the calculations volume.
The solutions will be handle more easily, quickly and elegantly without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions. In this approach the solution is found in the form of a convergent power series with easily computed components. The Adomian decomposition scheme is easy to program in applied problems and provides immediate and convergent solutions without any need for linearization or discretization. To give a clear overview of the methodology, we have selected illustrative example.

### MSC:

 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation
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