Optimal Order and Minimal Complexity of One-Step Methods for Initial Value Problems.

Abstract

We consider the task of numerically approximating the solution of an ordinary differential equation initial value problem. A methodology is given for determining the computational complexity of finding an approximate solution with error not exceeding epsilon. In addition, we determine the method of optimal order within a given class of methods, and show that under reasonable hypotheses, the optimal order increases as epsilon decreases, tending to infinity as epsilon tends to zero. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA035931

Entities

People

  • Arthur G. Werschulz

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Algorithms
  • Analytic Functions
  • Computational Complexity
  • Computations
  • Computer Science
  • Differential Equations
  • Equations
  • Iterations
  • Mathematics
  • New York
  • Numbers
  • Numerical Analysis
  • Partial Differential Equations
  • Polynomials
  • Real Numbers
  • Runge Kutta Method
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematics or Statistics