Numerical Method to Solve the Cauchy Problem with Previous History

Numerical Method to Solve the Cauchy Problem with Previous History

The paper analyzes the theoretical aspects of constructing a family of single-stage multi-step methods for solving the Cauchy problem with prehistory for ordinary differential equations. The authors consider general issues related to discretization, approximation, convergence, and stability. The pro...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Cybernetics and systems analysis 2017, Vol.53 (1), p.34-56
Hauptverfasser: Prusov, V. A., Doroshenko, A. Yu
Format: Artikel
Sprache:eng
Schlagworte:
Accuracy
Advection (Earth sciences)
Analysis
Approximation
Artificial Intelligence
Cauchy problem
Cauchy problems
Control
Convergence
Cybernetics
Differential equations
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Ordinary differential equations
Partial differential equations
Processor Architectures
Software Engineering/Programming and Operating Systems
Studies
Systems stability
Systems Theory
Velocity
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The paper analyzes the theoretical aspects of constructing a family of single-stage multi-step methods for solving the Cauchy problem with prehistory for ordinary differential equations. The authors consider general issues related to discretization, approximation, convergence, and stability. The problem of improving the accuracy of numerical solutions is analyzed in detail. The results presented in the paper are also applicable for the numerical solution of partial differential equations.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-017-9905-y