ISJ Theoretical & Applied Science 12(68) 2018

Philadelphia, USA

Abdirashidov, A., Karshiyev, A., Ortikov, B., & Kadirov, N.

Application of approximate adomian decomposition method and a variational iterations method to solving a Cauchy problem with the heat dissipation and Laplace equations.

Full Article: PDF

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-12-68-48

DOI: https://dx.doi.org/10.15863/TAS.2018.12.68.48

Language: English

Citation: Abdirashidov, A., Karshiyev, A., Ortikov, B., & Kadirov, N. (2018). Application of approximate adomian decomposition method and a variational iterations method to solving a Cauchy problem with the heat dissipation and Laplace equations. ISJ Theoretical & Applied Science, 12 (68), 323-329. Soi: http://s-o-i.org/1.1/TAS-12-68-48 Doi: https://dx.doi.org/10.15863/TAS.2018.12.68.48

Pages: 323-329

Published: 30.12.2018

Abstract: 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.

Key words: equations of heat dissipation and Laplace, Cauchy problem, variational iteration method, Adomian decomposition method, exact solutions.