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
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
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.
Received: 28 January 2008
Revised: 29 February 2008
Accepted manuscript online:
Fund: 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).
Cite this article:
Yang Pei(杨 沛), Chen Yong(陈勇), Li Zhi-Bin(李志斌) Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice 2008 Chin. Phys. B 17 3953
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
