Numerical comparison of methods for solving parabolic equations

摘要

In this paper, 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.