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Research Article | Open | Published:

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Abstract

We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

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Author information

Correspondence to Ravi P. Agarwal.

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation