Some Notes on the Convergence Control Parameter in the Framework of the Homotopy Analysis Method

The convergence control parameter and the technique of c0-curves is an unavoidable part of any homotopy analysis method work. The mathematical background of this parameter has been studied by other authors. Here we revisit this parameter and its essence; we mention that in some examples the parameter may fail to work. Also we give some comments in using the technique of c0-curves and show, through examples, that a misusage may lead the user to wrong results.