A Comparison Between the Adomian Decomposition and the Modified Crank-Nicholson Methods for the two-dimensional Burgers' Equation

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Haghighi A. R.; Ahmadishali J.; H. E. Alipur; Asghary N.

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Journal: JOURNAL OF MECHANICAL ENGINEERING Year:2019 | Volume:49 | Issue:2 (87) Page(s): 61-67

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Title

A Comparison Between the Adomian Decomposition and the Modified Crank-Nicholson Methods for the two-dimensional Burgers' Equation

Author(s)

Haghighi A. R. | Ahmadishali J. | H. E. Alipur | Asghary N. | Issue Writer Certificate

Keywords

Two–dimensional Burgers equation

Modified Local Crank-Nicholson method

Adomian decomposition method

Abstract

In this paper, numerical methods of the Adomian decomposition and the Modified Crank– Nicholson are used for solving the twodimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical solution. In contrast to the conventional Crank-Nicolson method, the MLCN method is an explicit and unconditionally stable method. This method leads to several block matrices through the transformation of the partial differential equation (PDE) into ordinary differential equations (ODE), which simplifies the calculations. 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. In this study velocity parameters u in the direction of the X axis, and v in the direction of the Y 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 compared utilizing two examples of trigonometric and exponential functions with different initial conditions, which shows that the Adomian decomposition method is closer to the analytical method.

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APA: Copy

Haghighi, A. R., Ahmadishali, J., , H. E. Alipur, & Asghary, N.. (2019). A Comparison Between the Adomian Decomposition and the Modified Crank-Nicholson Methods for the two-dimensional Burgers' Equation. JOURNAL OF MECHANICAL ENGINEERING, 49(2 (87) ), 61-67. SID. https://sid.ir/paper/270071/en

Vancouver: Copy

Haghighi A. R., Ahmadishali J., H. E. Alipur, Asghary N.. A Comparison Between the Adomian Decomposition and the Modified Crank-Nicholson Methods for the two-dimensional Burgers' Equation. JOURNAL OF MECHANICAL ENGINEERING[Internet]. 2019;49(2 (87) ):61-67. Available from: https://sid.ir/paper/270071/en

IEEE: Copy

A. R. Haghighi, J. Ahmadishali, H. E. Alipur , and N. Asghary, “A Comparison Between the Adomian Decomposition and the Modified Crank-Nicholson Methods for the two-dimensional Burgers' Equation,” JOURNAL OF MECHANICAL ENGINEERING, vol. 49, no. 2 (87) , pp. 61–67, 2019, [Online]. Available: https://sid.ir/paper/270071/en

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