APPLICATION OF APPROXIMATE ADOMIAN DECOMPOSITION METHOD AND A VARIATIONAL ITERATIONS METHOD TO SOLVING A CAUCHY PROBLEM WITH THE HEAT DISSIPATION AND LAPLACE EQUATIONS
Ablakul AbdirashidovAbduvali KarshiyevCandidate of Physical and Mathematical Sciences, Head of department of Computer engineering, Tashkent university information technology Samarkand State University, UzbekistanBekzod OrtikovCandidate of Physical and Mathematical Sciences, Head of department of Computer engineering, Tashkent university information technology Samarkand State University, UzbekistanNurshod KadirovStudent of Mechanical and Mathematical Faculty, Samarkand State University, Uzbekistan
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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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