Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients.

Abstract

A general theory for nonlinear implicit one-step schemes for solving initial value problems for ordinary differential equations is presented in this paper. The general expansion of 'symmetric' implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. Based on previous work of the first author on a Generalization of Means, a fourth-order nonlinear implicit one-step scheme (GMS) is presented for solving equations with steep gradients. Also, a hybrid method based on the GMS and a fourth-order linear scheme is discussed. Some numerical results are given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1982
Accession Number
ADA122615

Entities

People

  • Jiachang Sun
  • Ken Jackson

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Arithmetic
  • Boundaries
  • Boundary Value Problems
  • Computer Science
  • Convergence
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Errors
  • Exponential Functions
  • Interpolation
  • Iterations
  • Numbers
  • Polynomials
  • Quadratic Equations
  • Theorems

Fields of Study

  • Mathematics

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