NON-LINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS AND DIFFERENCE EQUATIONS

Abstract

The Dirichlet problem for the non-linear elliptic partial differential equation a(x,y,u(x,y))u, sub xx + c(x,y,u(x,y))u, sub yy - gamma(x, y,u(x,y))u = O is studied. It is assumed that the coefficients are strictly positive and Lipschitz in the argument u(x,y). It is then proved that the solution may be uniformly approximated by the solution to the associated difference equation provide ed that a certain inequality, relating bounds on the coefficients, is satisfied.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1963
Accession Number
AD0424182

Entities

People

  • Gregory T. Mcallister

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Difference Equations
  • Differential Equations
  • Equations
  • Inequalities
  • Maryland
  • Mathematics
  • Military Research
  • New York
  • North Carolina
  • Partial Differential Equations
  • Point Theorem
  • Sequences
  • Space Flight

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research