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In this paper, the Cauchy problem with the heat dissipation and Laplace equations is solved analytically using the Adomian decomposition method and the variational iteration method. It is shown that these methods are the most effective and convenient for solving some evolution equations. The obtained approximate solutions were compared, the results of these methods are the same; while the method of decomposition of Adomian can be much simpler, more convenient and more efficient to approach such problems as compared to the method of variational iteration and other traditional methods.

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APPLICATION OF APPROXIMATE ADOMIAN DECOMPOSITION METHOD AND A VARIATIONAL ITERATIONS METHOD TO SOLVING A CAUCHY PROBLEM WITH THE HEAT DISSIPATION AND LAPLACE EQUATIONS