SOME NUMERICAL EXPERIMENTS USING NEWTON'S METHOD FOR NONLINEAR PARABOLIC AND ELLIPTIC BOUNDARY-VALUE PROBLEMS

Abstract

Using a generalization of Newton's method, a nonlinear parabolic equation of the form u sub t - u sub xx = g(u), and a nonlinear elliptic equation u sub xx + u sub yy = e superscript u, are solved numerically. Comparison of these results with results obtained using the Picard iteration procedure show that in many cases the quasilinearization method offers substantial advantages in both time and accuracy.

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Document Details

Document Type
Technical Report
Publication Date
Jan 23, 1961
Accession Number
AD0676653

Entities

People

  • Mario Juncosa
  • Richard E. Bellman
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Calculus Of Variations
  • Computer Science
  • Convergence
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Equations
  • Errors
  • Integral Equations
  • Iterations
  • Linear Differential Equations
  • Partial Differential Equations
  • Triangles
  • Truncation

Fields of Study

  • Mathematics

Readers

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