On Reusing the Stages of a Rejected Runge-Kutta Step-Reference-Cited by-同舟云学术

On Reusing the Stages of a Rejected Runge-Kutta Step

Published:2023-06-05 Issue:11 Volume:11 Page:2589
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Kovalnogov Vladislav N.¹,Fedorov Ruslan V.¹^ORCID,Karpukhina Tamara V.¹,Simos Theodore E.¹²³⁴⁵⁶^ORCID,Tsitouras Charalampos⁷^ORCID

Affiliation:

1. Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia

2. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref 32093, Kuwait

3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan

4. Data Recovery Key Laboratory of Sichun Province, Neijiang Normal University, Neijiang 641100, China

5. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece

6. Department of Mathematics, University of Western Macedonia, 50100 Kozani, Greece

7. General Department, National & Kapodistrian University of Athens, Euripus Campus, 34400 Evia, Greece

Abstract

Runge-Kutta (RK) pairs are amongst the most popular methods for numerically solving Initial Value Problems. While using an RK pair, we may experience rejection of some steps through the interval of integration. Traditionally, all of the evaluations are then dropped, and we proceed with a completely new round of computations. In this work, we propose avoiding this waste and continuing by reusing the rejected RK stages. We focus especially on an RK pair of orders six and five. After step rejection, we reuse all the previously evaluated stages and only add three new stages. We proceed by evaluating the output using a smaller step. By this technique, we manage to significantly reduce the cost in a set of problems that are known to pose difficulties in RK algorithms with changing step sizes.

Funder

Mega Grant from the Government of the Russian Federation within the framework of federal project

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/11/2589/pdf

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