Dimensional Reduction for Nonlinear Boundary Value Problems.

Abstract

This paper elaborates on the method of dimensional reduction for nonlinear problems which transforms the 2 dimensional problem into a system of ordinary differential equations in an optimal way. Numerical example illustrates the approach. Contents: Introduction; Notation and model problem; The Galerkin approach to dimensional reduction; Asymptotic expansions (for the selection of basis functions); The selection of basis functions; The optimality of above selection of basis functions (at fixed N); Optimal convergence for increasing number of reduced models (at fixed e); and Computational results.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1986
Accession Number
ADA173513

Entities

People

  • Ivo Babuška
  • Soren Jensen

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computations
  • Convergence
  • Differential Equations
  • Equations
  • Errors
  • Hypotheses
  • Inequalities
  • Military Research
  • Partial Differential Equations
  • Physical Sciences
  • Standards
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Structural Dynamics.
  • Systems Analysis and Design