Spline-Based Parameter Estimation Techniques for Two-Dimensional Convection and Diffusion Equations.

Abstract

A general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two-dimensional convection and diffusion equations derived from mass transport theory. The parameter estimation problem is first cast as an abstract infinite dimensional minimization problem. Then a sequence of approximate, finite dimensional problems is defined, which yields a sequence of parameter estimates. Convergence results relating the approximate problems to the full infinite dimensional problem are presented, as well as a discussion addressing computer implementation. Finally, the technique is applied to the analysis of actual biological data from an insect dispersal experiment, in which the movement of cabbage root flies in the presence of a cabbage crop was studied. It is proposed that such a parameter estimation method can be a useful analytical tool to help develop appropriate models in population biology.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA181925

Entities

People

  • L. L. Zia

Organizations

  • Brown University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Banach Space
  • Boltzmann Equation
  • Computations
  • Convection
  • Differential Equations
  • Diffusion
  • Equations
  • Experimental Design
  • Mathematical Analysis
  • Models
  • Partial Differential Equations
  • Standards
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Aquatic Ecology