Numerical solution of the one dimensional non-linear Burgers equation using the Adomian decomposition method and the comparison between the modified Local Crank-Nicolson method and the VIM exact solution
Publish Year: 1394
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJIM-7-2_004
تاریخ نمایه سازی: 27 دی 1402
Abstract:
The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to the conventional Crank-Nicolson method, the MLCN method is an explicit and unconditionally stable method. The Adomian decomposition method includes the unknown function U (x), in which each equation is defined and solved by an infinite series of unbounded functions. Velocity parameters u in the direction of the X axis, are examined at different times with different Reynolds numbers over a fixed time step. Also the accuracy of the Adomian and the Crank-Nicolson methods at different Reynolds numbers have been studied using two examples with different initial conditions, and the Adomian decomposition method is closer to the analytical method.
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Authors
AR. Haghighi
Department of Mathematics, Urmia University of Technology, Urmia, Iran.
M. Shojaeifard
Department of Mathematics, Urmia University of Technology, Urmia, Iran.