A Look at Some Methods of Solving Partial Differential Equations and Eigenvalue Problems

Abstract

Four techniques for the numerical solution of partial differential equations and eigenvalue problems were investigated. Typical problems considered were elliptic partial differential equations of the form U sub xx + U sub yy = f(x,y), or U sub xx + U sub yy + lambda squared U = O, where appropriate boundary conditions are specified so that the problem is self-adjoint. The four methods are relaxation, Galerkin, Rayleigh-Ritz, and dynamic programming combined with Stodola'a method, for eigenvalue problems. The results indicated that for eigenvalue problems relaxation or dynamic programming modified is to be preferred usually and for partial differential equations Galerkin or dynamic programming is preferred.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1972
Accession Number
AD0742920

Entities

People

  • Edward Leon Bloxom

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Calculus
  • Calculus Of Variations
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computer Programs
  • Computers
  • Difference Equations
  • Differential Equations
  • Dynamic Programming
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Euler Equations
  • Kinetic Energy
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Operations Research