ON THE CRANK-NICOLSON PROCEDURE FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS,

Abstract

Proof of convergence of the Crank-Nicolson procedure, an 'implicit' numerical method for solving parabolic partial differential equations, is given for the case of the classical 'problem of limits' for one-dimensional diffusion with zero boundary conditions. Orders of convergence are also given for different classes of initial functions. Results do not support the validity of socalled 'h2-extrapolation' in some cases. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 13, 1954
Accession Number
AD0604289

Entities

People

  • David L. Young
  • M. L. Juncosa

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Convergence
  • Differential Equations
  • Diffusion
  • Equations
  • Extrapolation
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.