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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 19, Issue 7-8


L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems

Sania Qureshi
  • Corresponding author
  • Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
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  • De Gruyter OnlineGoogle Scholar
/ Higinio RamosORCID iD: http://orcid.org/0000-0003-2791-6230
Published Online: 2018-10-23 | DOI: https://doi.org/10.1515/ijnsns-2017-0267


In this work, we develop a nonlinear explicit method suitable for both autonomous and non-autonomous type of initial value problems in Ordinary Differential Equations (ODEs). The method is found to be third order accurate having L-stability. It is shown that if a variable step-size strategy is employed then the performance of the proposed method is further improved in comparison with other methods of same nature and order. The method is shown to be working well for initial value problems having singular solutions, singularly perturbed and stiff problems, and blow-up ODE problems, which is illustrated using a few numerical experiments.

Keywords: nonlinear explicit method; rational approximation; blow-up ODEs; singular solutions; L-Stability; variablestep-size

PACS: 65Lxx; 65L04; 65L05; 65L11; 65L12


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About the article

Received: 2017-12-07

Accepted: 2018-10-05

Published Online: 2018-10-23

Published in Print: 2018-12-19

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 741–751, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0267.

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