Almost Periodic Solutions to Difference Equations

Abstract

The theory of Massera and Schaffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation has been completely extended to discretizations by a strongly stable difference scheme. In addition it has been shown that the almost periodic sequence solution will converge to the differential equation solution at a rate O(k sup p) where p is the accuracy of the scheme, uniformly in t, if the coefficients are sufficiently smooth. The preceding theory has also been applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida Theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation which can be approximated by almost periodic sequences which are the solutions to appropriate discretizations. Two methods of discretizations are discussed; the strongly stable scheme described above and the Lax-Wendroff scheme.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1975
Accession Number
ADA011674

Entities

People

  • Alvin Bayliss

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Analogs
  • Banach Space
  • Coefficients
  • Continuity
  • Convergence
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Errors
  • Identities
  • Inequalities
  • Integral Equations
  • New York
  • Partial Differential Equations
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)