中国物理B ›› 2008, Vol. 17 ›› Issue (11): 3953-3964.doi: 10.1088/1674-1056/17/11/005
杨 沛1, 李志斌2, 陈 勇3
Yang Pei(杨沛)a, Chen Yong(陈勇)b, Li Zhi-Bin(李志斌)ab
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.
中图分类号: (Lattice theory and statistics)