A Class of Hybrid Multistep Block Methods with A –Stability for the Numerical Solution of Stiff Ordinary Differential Equations

Zarina Bibi Ibrahim and Amiratul Ashikin Nasarudin
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Zarina Bibi Ibrahim: Dept of Mathematics, Faculty of Science, Serdang 43400 UPM, Malaysia
Amiratul Ashikin Nasarudin: Institute for Mathematical Research, Dept of Mathematics, Faculty of Science, Serdang 43400 UPM, Malaysia

Mathematics, 2020, vol. 8, issue 6, 1-19

Abstract: Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy.

Keywords: A –stability; consistent; zero-stable; stiff (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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