| Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice |
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| 引用本文： | 杨 沛,陈 勇,李志斌.Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice[J].中国物理 B,2008,17(11):3953-3964. |
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| 作者姓名： | 杨 沛 陈 勇 李志斌 |
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| 作者单位： | Department of Computer Science, East China
Normal
University, Shanghai 200241, China;Shanghai Key Laboratory of Trustworthy Computing, East
China Normal University, Shanghai 200062, China;Department of Computer Science, East China
Normal
University, Shanghai 200241, China；Shanghai Key Laboratory of Trustworthy Computing, East
China Normal University, Shanghai 200062, China |
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| 基金项目： | Project supported by the National
Key Basic Research Project of China (Grant No 2004CB318000), the
National Natural Science Foundation of China (Grant Nos 10771072 and
10735030), and Shanghai Leading Academic Discipline Project of China
(Grant No B412). |
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| 摘 要： | The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.
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| 关 键 词： | 数学物理方法 Blaszak-Marciniak点阵 孤波解 分解方法 |
| 收稿时间： | 2008-01-28 |
Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice |
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| Yang Pei,Chen Yong and Li Zhi-Bin.Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice[J].Chinese Physics B,2008,17(11):3953-3964. |
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| Authors: | Yang Pei Chen Yong and Li Zhi-Bin |
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| Institution: | Department of Computer Science, East China
Normal
University, Shanghai 200241, China; Department of Computer Science, East China
Normal
University, Shanghai 200241, China；Shanghai Key Laboratory of Trustworthy Computing, East
China Normal University, Shanghai 200062, China; Shanghai Key Laboratory of Trustworthy Computing, East
China Normal University, Shanghai 200062, China |
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| Abstract: | The Adomian decomposition method (ADM) and Pad\'{e} approximants are
combined to solve the well-known Blaszak--Marciniak lattice, which
has rich mathematical structures and many important applications in
physics and mathematics. In some cases, the truncated series
solution of ADM is adequate only in a small region when the exact
solution is not reached. To overcome the drawback, the Pad\'{e}
approximants, which have the advantage in turning the polynomials
approximation into a rational function, are applied to the series
solution to improve the accuracy and enlarge the convergence domain.
By using the ADM-Pad\'{e} technique, the soliton solutions of the
Blaszak--Marciniak lattice are constructed with better accuracy and
better convergence than by using the ADM alone. Numerical and
figurative illustrations show that it is a promising tool for
solving nonlinear problems. |
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| Keywords: | Adomian decomposition method Pad\'{e} approximants Blaszak--Marciniak lattice soliton solution |
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