Numerical Methods for Stiff, Quadratic and Josephson Interferometer Differential Equations.

Abstract

THE TWO-PARAMETER CLASS OF ALL A-contractive two-step second-order formulas was derived for arbitrary step ratios. Similarly, the one-parameter class of all A-constractive two-step second-order formulas was derived for arbitrary step ratios. A specific A-contractive formula was derived which minimizes a measure of the global truncation error. The one-leg implementation of the S-contractive formulas provides A-stable methods for x = Lambda(t)x for any Lambda(t), Re Lambda(t) < or = 0 and any step sequence (hn). It was shown that, among all A-stable two-step second-order formulas for uniform steps, the A-constractive formulas are the only ones for which A-stability is conserved under any sufficiently small perturbation of the uniformity of the steps. An efficient numerical study, as well as perturbation analysis of the solutions to the two-junction interferometer was carried out.

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Document Details

Document Type
Technical Report
Publication Date
Aug 31, 1980
Accession Number
ADA111503

Entities

People

  • F. Odeh
  • W. Liniger

Organizations

  • IBM Thomas J. Watson Research Center

Tags

Communities of Interest

  • Air Platforms
  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Difference Equations
  • Differential Equations
  • Equations
  • Errors
  • Interferometers
  • Josephson Junctions
  • Linear Systems
  • Materials
  • Nonlinear Differential Equations
  • Nonlinear Systems
  • Perturbations
  • Resonance
  • Resonant Frequency
  • Sequences
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra