DOI: https://doi.org/10.26089/NumMet.v16r342

A variable structure algorithm using the (3,2)-scheme and the Fehlberg method

Authors

  • E.A. Novikov

Keywords:

stiff systems
k)-schemes
Fehlberg method
Runge–Kutta methods
accuracy and stability control
variable structure algorithm
ordinary differential equations
numerical methods

Abstract

A third-order (3,2)-method allowing freezing the Jacobi matrix is constructed. Its main and intermediate numerical schemes are L-stable. An accuracy control inequality is obtained using an embedded method of second order. A stability control inequality for the explicit three-stage Runge-Kutta-Fehlberg method of third order is proposed. A variable structure algorithm is formulated. An explicit or L-stable method is chosen according to the stability criterion at each step. Numerical results are discussed.

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Published

2015-08-09

Issue

Vol. 16 (2015): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biography

E.A. Novikov

Institute of Computational Modeling of SB RAS (ICM SB RAS)
• Chief Researcher

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