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

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.