Stability of Two-Step Methods for Variable Integration Steps.

Abstract

Two of the most commonly used methods, the Trapezoidal Rule and the two-step backward differentiation formula, both have drawbacks when applied to difficult stiff problems. The Trapezoidal Rule does not sufficiently damp the stiff components and the backward differentiation method is unstable for rapidly varying steps. In this paper we show that there exists a one-parameter family of two-steps, second-order one-leg methods which are stable for any test problem, using arbitrary step sequences. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1980
Accession Number
ADA098139

Entities

People

  • Germund G. Dahlquist
  • Olavi Nevanlinna
  • Werner Linigier

Organizations

  • IBM Thomas J. Watson Research Center

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Fields of Study

  • Mathematics

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