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| Adomian decomposition method for solving two dimensional Helmholtz equations |
| Received:October 10, 2012 Revised:December 24, 2012 |
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| DOI：10.7511/jslx201401007 |
| KeyWord:Helmholtz equations Adomian decomposition method exact solutions convergence |
| Author | Institution |
| 毛崎波 |
南昌航空大学 飞行器工程学院, 南昌 |
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| Abstract: |
| The Adomian decomposition method (ADM) is employed in this paper to solve two dimensional Helmholtz equations.Based on the ADM the Helmholtz differential equation becomes a recursive algebraic equation.Furthermore,the boundary conditions become simple algebraic equations which are suitable for symbolic computation.By using boundary conditions,the closed-form series solution can be easily obtained.The main advantages of ADM are computational simplicity and do not involve any linearization or discretization.Finally,several computed examples are presented to check the reliability of the method.Comparing the results using ADM to the exact solutions,excellent agreement is achieved.The numerical results demonstrate that the ADM is quite accurate and readily implemented.Furthermore,the good convergence and the excellent numerical stability of the solution based on the ADM can also be found.It means that the ADM is quite efficient and is practically well suited for solving two dimensional Helmholtz equations. |