Rational homotopy perturbation method
Summary: The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to results obtained by the HPM method. For the second example, which is a Van der Pol oscillator problem, we compare RHPM, HPM, and VIM, finding out that RHPM method generates the most accurate approximated solution.
scientific article; zbMATH DE number 6106225