Journal
NONLINEAR DYNAMICS
Volume 94, Issue 2, Pages 873-888Publisher
SPRINGER
DOI: 10.1007/s11071-018-4399-3
Keywords
Renormalization method; Homotopy renormalization method; Asymptotic analysis; Newton-Maclaurin expansion; Difference equation
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The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic theorems on the renormalization method are proven. Some interesting applications are given, including asymptotic solutions of quantum anharmonic oscillator and discrete boundary layer, the reductions and invariant manifolds of some discrete dynamics systems. Furthermore, the homotopy renormalization method based on the Newton-Maclaurin expansion is proposed and applied to those difference equations including no a small parameter. In addition, some subtle problems on the renormalization method are discussed.
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