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Numerical comparison of methods for solving parabolic equations. (English) Zbl 1061.65098

Summary: We apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:

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