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| A comparison of the after-treatment techniques for Adomian modified decomposition method |
| Received:April 27, 2016 Revised:January 31, 2017 |
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| DOI：10.7511/jslx201704019 |
| KeyWord:Adomian modified decomposition method after-treatment techniques Padé approximant method Laplace-Padé approximant multistage method |
| Author | Institution |
| 毛崎波 |
扬州大学 机械工程学院, 扬州 ;南昌航空大学 飞行器工程学院, 南昌 |
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| Abstract: |
| The theory of the Adomian modified decomposition method (AMDM) for solving nonlinear differential equations is well established.The main advantages of AMDM are computational simplicity and no involvement of any linearization or discretization.However,the accuracy of the AMDM solution depends on the convergence region.To extend the convergence region of the AMDM,several after-treatment techniques (such as Padé approximant,Laplace-Padé approximant and multistage method) have been proposed to improve the accuracy of the AMDM on a wide region.In this study,first,a brief review of the AMDM is given.Then these three after-treatment techniques are discussed.Finally,with examples of free and force Duffing oscillator problems,numerical results are presented to compare the drawbacks and advantages of these after-treatment techniques.It is shown that the multistage after-treatment technique offers an accurate and effective method for solving nonlinear differential equations in a wide applicable region. |