Rational Homotopy Perturbation Method
Copyright policy )Rational Homotopy Perturbation Method
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.
- Universidad Veracruzana Mexico
Poincaré–Lindstedt method, rational homotopy perturbation method, Mathematical analysis, Quantum mechanics, Convergence Analysis of Iterative Methods for Nonlinear Equations, Higher-Order Methods, Differential equation, Perturbation (astronomy), Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, Parameter-Robust Methods, Homotopy perturbation method, Singular perturbation, Anomalous Diffusion Modeling and Analysis, nonlinear differential equations, Numerical Analysis, Physics, Pure mathematics, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Applied mathematics, Homotopy analysis method, Van der Pol oscillator, Modeling and Simulation, Physical Sciences, Nonlinear system, Numerical methods for ordinary differential equations, Homotopy Analysis Method, Homotopy, Iterative Methods, Mathematics
Poincaré–Lindstedt method, rational homotopy perturbation method, Mathematical analysis, Quantum mechanics, Convergence Analysis of Iterative Methods for Nonlinear Equations, Higher-Order Methods, Differential equation, Perturbation (astronomy), Numerical Methods for Singularly Perturbed Problems, QA1-939, FOS: Mathematics, Parameter-Robust Methods, Homotopy perturbation method, Singular perturbation, Anomalous Diffusion Modeling and Analysis, nonlinear differential equations, Numerical Analysis, Physics, Pure mathematics, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Applied mathematics, Homotopy analysis method, Van der Pol oscillator, Modeling and Simulation, Physical Sciences, Nonlinear system, Numerical methods for ordinary differential equations, Homotopy Analysis Method, Homotopy, Iterative Methods, Mathematics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).16 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!