A note on effect of linear operator on the improvement of the convergence of an approximate solution using homotopy analysis method

This paper mainly focuses on the utilization of freedom given by homotopy analysis method to improve the convergence of an approximate solution. Here we use the idea of freedom of choice of linear operator and base function which is one of the advantages of HAM over previous techniques. We applied this idea on two nonlinear problems chosen as examples. Results are given with error analysis for different linear operators and base functions. We proved that convergence for nonlinear problems can be improved by using the freedom of choice of linear operator and base function. Our results agree well with the results of homotopy-Pad́e approximations.