AN EFFICIENT TECHNIQUE FOR SOLVING THE BLASZAK–MARCINIAK LATTICE BY COMBINING HOMOTOPY PERTURBATION AND PADÉ TECHNIQUES

Abstract

We combined the Homotopy perturbation method (HPM) and Padé techniques to solve the well-known Blaszak–Marciniak lattice. Blaszak–Marciniak lattice has rich mathematical structures and many important applications in physics, engineering and mathematics. Generally, the truncated series solution of HPM is adequate only in a small region when the exact solution is not reached. We overcame this limitation by using the Padé techniques, 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. Using this combined technique, the soliton solutions of the Blaszak–Marciniak lattice are constructed with better accuracy and better convergence than by using the HPM alone. An example of computed calculation is followed by comparative plots of the solutions obtained through the (HPM) and (HPM-Padé) methods. Graphics are gathered for discussion of convergence. The same protocol is applied to Blaszak–Marciniak four-field lattice.