RUNGE-KUTTA TYPE PROCEDURES OF ORDER OF ACCURACY N + 4 (N>2) WITH THREE NODES FOR NUMERICAL INTEGRATION OF FIRST-ORDER DIFFERENTIAL EQUATIONS,

Abstract

By transformation, E. Fehlberg reduced integration of a first-order differential equation: dz/dx=F(x,z), with initial condition: z(x sub 0) =z sub 0, to integration of another first-order differential equation. This allows the establishment of Runge-Kutta type operations of sixth-order accuracy for numerical integration of the transformed differential equation. In the first part of this paper the Fehlberg transformation is extended to allow the establishment of Runge-Kutta procedures of eighth-order accuracy with three nodes for numerical integration of the transformed differential equation. Then the above transformations are generalized to permit establishment of Runge-Kutta procedures of order of accuracy n+4 (n>or =2) with three nodes for numerical integration of the transformed differential equation. The nodes and coefficients in the formulas used for application of these procedures are rational numbers.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0609692

Entities

People

  • A. Cotiu

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Coefficients
  • Differential Equations
  • Equations
  • Mathematics
  • Numbers
  • Numerical Integration
  • Rational Numbers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)