A High Order WENO Scheme for a Hierarchical Size-Structured Model

Abstract

In this paper we develop a high order explicit finite difference weighted essentially non-oscillatory (WENO) scheme for solving a hierarchical size-structured population model with nonlinear growth, mortality and reproduction rates. The main technical complication is the existence of global terms in the coefficient and boundary condition for this model. We carefully design approximations to these global terms and boundary conditions to ensure high order accuracy. Comparing with the first order monotone and second order total variation bounded schemes for the same model, the high WENO scheme is more efficient and can produce accurate results with far fewer grid points. Numerical examples including one in computational biology for the evolution of the population of Gambussia affinis, are presented to illustrate the good performance of the high order WENO scheme.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA468112

Entities

People

  • Chi-Wang Shu
  • Jun Shen
  • Mengping Zhang

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Applied Mathematics
  • Boundaries
  • Coefficients
  • Computational Biology
  • Computational Fluid Dynamics
  • Differential Equations
  • Discontinuities
  • Electronic Mail
  • Environment
  • Equations
  • Errors
  • Fluid Dynamics
  • High Resolution
  • Mathematics
  • Simulations

Fields of Study

  • Mathematics

Readers

  • Aquatic Ecology
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)