Numerical solution of a nonlinear diffusion model with memory

Abstract

Finite difference approximation of a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Here we discuss the model described by a nonlinear integro-differential equation. The system of time dependent ordinary differential equations is solved using Runge-Kutta method with adaptive step size. The time integral make this a non-trivial application of the Matlab code ODE45. Eight examples are given with mostly homogeneous boundary conditions. The results show that when the analytic solution is not growing in time, then the solution decays at a rate proven theoretically in the literature.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2018
Accession Number
AD1073569

Entities

People

  • Benjamin R Anderson
  • Beny Neta
  • Grant D. Thornton
  • Grant M. Robertson
  • Jessica Shapiro
  • Matthew A. Baugh
  • Robert C. Thyberg

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Chemistry
  • Department Of Defense
  • Differential Equations
  • Diffusion
  • Equations
  • Grids
  • Heat Capacity
  • Information Operations
  • Integrals
  • Literature
  • Magnetic Fields
  • Mathematical Analysis
  • Mathematics
  • New York
  • Nonlinear Systems
  • Numerical Analysis
  • Partial Differential Equations
  • Real Variables
  • Runge Kutta Method
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics