Block Implicit One-Step Methods,

Abstract

A new class of block implicit one-step methods for ordinary differential equations is presented. The methods are based on quadrature and generate function values at nonmesh quadrature points through Hermite interpolation. A general convergence theorem for block implicit methods is proved, and the stability of the new class of methods is analyzed. The class is shown to contain A-stable, stiffly stable, strongly A-stable, and strongly stiffly stable methods. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1972
Accession Number
AD0746390

Entities

People

  • D. S. Watanabe

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Convergence
  • Differential Equations
  • Equations
  • Interpolation
  • Mathematics

Fields of Study

  • Mathematics

Readers

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