Preprint Article Version 1 NOT YET PEER-REVIEWED

Numerical stability of the multi-step methods to solve the stiff equation by using the CADNA library

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, 14676-86831, Tehran, Iran
Version 1 : Received: 13 July 2016 / Approved: 14 July 2016 / Online: 14 July 2016 (04:47:26 CEST)

How to cite: Barzegar, H.; Fariborzi Araghi, M. Numerical stability of the multi-step methods to solve the stiff equation by using the CADNA library. Preprints 2016, 2016070027 (doi: 10.20944/preprints201607.0027.v1). Barzegar, H.; Fariborzi Araghi, M. Numerical stability of the multi-step methods to solve the stiff equation by using the CADNA library. Preprints 2016, 2016070027 (doi: 10.20944/preprints201607.0027.v1).

Abstract

In this paper, based on the stochastic arithmetic, the accuracy and stability of multi-step methods to solve the stiff differential equation is studied. By using the CESTAC method and the CADNA library, the optimal iterate and the optimal step size of the multi-step methods can be dynamically computed and its accuracy can be estimated. Also, numerical stability of the multi-step methods to solve the stiff equation will be considered. For this purpose, a theorem is proved to show the accuracy of the results via the concept of the common significant digits between two sequential results. Finally, two numerical examples are given to show the efficiency and advantages of using the CADNA library.

Subject Areas

Stochastic Arithmetic, CESTAC method, CADNA library, Multi-step methods, Stiff differential equation

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