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Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5098–5112 | Cite as

Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs

  • B. Behzad
  • B. Ghazanfari
  • A. Abdi
Article
  • 31 Downloads

Abstract

In this paper, we study the construction and implementation of special Nordsieck second derivative general linear methods of order p and stage order \(q=p\) in which the number of input and output values is \(r=p\) rather than \(r=p+1\). We will construct A- and L-stable methods of orders three and four in this form with Runge–Kutta stability properties. The efficiency of the constructed methods and reliability of the proposed error estimates are shown by implementing of the methods in a variable stepsize environment on some well-known stiff problems.

Keywords

Stiff differential equations Second derivative methods Nordsieck methods Runge–Kutta stability A and L stability Variable stepsize 

Mathematics Subject Classification

65L05 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Department of MathematicsLorestan UniversityKhorramabadIran
  2. 2.Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

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