中国物理B ›› 2008, Vol. 17 ›› Issue (11): 3953-3964.doi: 10.1088/1674-1056/17/11/005

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Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

杨 沛1, 李志斌2, 陈 勇3   

  1. (1)Department of Computer Science, East China Normal University, Shanghai 200241, China; (2)Department of Computer Science, East China Normal University, Shanghai 200241, China；Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; (3)Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
  • 收稿日期:2008-01-28 修回日期:2008-02-29 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    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).

Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

Yang Pei(杨沛)a, Chen Yong(陈勇)b,  Li Zhi-Bin(李志斌)ab   

  1. a Department of Computer Science, East China Normal University, Shanghai 200241, China; b Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
  • Received:2008-01-28 Revised:2008-02-29 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    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 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.

关键词: Adomian decomposition method, Pad\'{e} approximants, Blaszak--Marciniak lattice, soliton solution

Abstract: The Adomian decomposition method (ADM) and Padé 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 Padé 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-Padé 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.

Key words: Adomian decomposition method, Padé approximants, Blaszak--Marciniak lattice, soliton solution

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
02.30.Mv (Approximations and expansions) 05.45.Yv (Solitons)