Approximate solution for system of differential-difference equations by means of the homotopy analysis method (Q618112)

The author applies the homotopy analysis method (HAM) to the solution of a system of differential-difference equations and to a Toda lattice system. The paper provides background information on HAM, shows how the method can be generalised to differential-difference equations and Toda lattice systems and finally considers some convergence results on the performance of the method. The conclusion drawn in the paper is that if the series solution converges, then it converges to an exact solution.