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

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HAGHIGHI A.R.; SHOJAEIFARD M.

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2015 | Volume:7 | Issue:2 Page(s): 149-159

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Title

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

Author(s)

HAGHIGHI A.R. | SHOJAEIFARD M. | Issue Writer Certificate

Keywords

NON-LINEAR BURGERS EQUATIONQ2

ADOMIAN METHODQ2

THE MODIFIED LOCAL CRANK-NICOLSON ‎METHODQ2

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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References

SPECIAL SOLITONIC LOCALIZED STRUCTURES FOR THE ONE-DIMENSIONAL BURGERS EQUATION IN WATER WAVES

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APA: Copy

HAGHIGHI, A.R., & SHOJAEIFARD, M.. (2015). 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. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 7(2), 149-159. SID. https://sid.ir/paper/231773/en

Vancouver: Copy

HAGHIGHI A.R., SHOJAEIFARD M.. 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. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2015;7(2):149-159. Available from: https://sid.ir/paper/231773/en

IEEE: Copy

A.R. HAGHIGHI, and M. SHOJAEIFARD, “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,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 7, no. 2, pp. 149–159, 2015, [Online]. Available: https://sid.ir/paper/231773/en

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