Power Series Methods I - Ordinary Differential Equations.

Abstract

A method is presented for constructing finite difference schemes of high accuracy for ordinary differential equations. Since it is based on power series representation of the solution it is applicable to partial differential equations as well. The method is demonstrated on the general nonlinear first order ordinary differential equation and the truncation errors are analysed. A-stability of the method is analysed and it is found to be stable in this sense to arbitrarily high order. Finally a nonlinear example is presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1979
Accession Number
ADA068939

Entities

People

  • Robert D. Small

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Computations
  • Contracts
  • Difference Equations
  • Differential Equations
  • Equations
  • Errors
  • Inequalities
  • Mathematics
  • North Carolina
  • Numerical Analysis
  • Partial Differential Equations
  • Power Series
  • Sequences
  • Smoothing (Mathematics)
  • Truncation
  • United States

Fields of Study

  • Mathematics

Readers

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