<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number of calculations required and the amount of work involved to obtain the approximate values of the exact solution of a certain problem for a given set of points, within a prescribed computational accuracy, is proportional to the number of accomplished iterations. We perform an analysis of the local truncation error and we derive an adaptive stepsize algorithm which coupled with a certain one-step numerical method makes the use of this structure more computationally effective and insures that the estimated values of the exact solution are in agreement with an imposed accuracy. We conclude with numerical computations proving the efficiency of the proposed step selection algorithm.</p></abstract>

The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number of calculations required and the amount of work involved to obtain the approximate values of the exact solution of a certain problem for a given set of points, within a prescribed computational accuracy, is proportional to the number of accomplished iterations. We perform an analysis of the local truncation error and we derive an adaptive stepsize algorithm which coupled with a certain one-step numerical method makes the use of this structure more computationally effective and insures that the estimated values of the exact solution are in agreement with an imposed accuracy. We conclude with numerical computations proving the efficiency of the proposed step selection algorithm.

An adaptive stepsize algorithm for the numerical solving of initial-value problems

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start...

An adaptive stepsize algorithm for the numerical solving of initial-value problems

Published Online: Apr 04, 2017

Page range: 185 - 198

Received: May 02, 2014

Accepted: Jun 28, 2014

DOI: https://doi.org/10.1515/auom-2015-0012

Keywords
initial value problems, adaptive numerical methods, local truncation error approach, one-step numerical methods, numerical computation

© 2015 Romulus Militaru, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An adaptive stepsize algorithm for the numerical solving of initial-value problems

Published Online: Apr 04, 2017

Page range: 185 - 198

Received: May 02, 2014

Accepted: Jun 28, 2014

DOI: https://doi.org/10.1515/auom-2015-0012

Keywordsinitial value problems, adaptive numerical methods, local truncation error approach, one-step numerical methods, numerical computation

© 2015 Romulus Militaru, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
initial value problems, adaptive numerical methods, local truncation error approach, one-step numerical methods, numerical computation