Equivalent Forms of Multistep Formulas.

Abstract

For uniform meshes it is shown that any linear k-step formula can be formulated so that only k values need to be saved between steps. By saving an additional m values it is possible to construct local polynomial approximations of degree k+m-1, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local monomial bases yield Nordsieck formulas. An explicit one-to-one correspondence is established between Nordsieck formulas and k-step-formulas of order at least k, and a strong equivalence result is proved for all but certain pathological cases. Equivalence is also shown for P(EC)* formulas but not for P(EC)*E formulas. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1978
Accession Number
ADA062737

Entities

People

  • Robert D. Skeel

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Computations
  • Computer Programs
  • Computer Science
  • Computers
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Eigenvalues
  • Equations
  • Illinois
  • Intellectual Property
  • Numerical Integration
  • Scientific Research
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.