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A new formulae of variable step 3-point block BDF method for solving stiff ODEs

Abasi, Naghmeh and Suleiman, Mohamed and Ismail, Fudziah and Ibrahim, Zarina Bibi and Musa, Hamisu and Abbasi, Neda (2014) A new formulae of variable step 3-point block BDF method for solving stiff ODEs. Journal of Pure and Applied Mathematics: Advances and Applications, 12 (1). pp. 49-76. ISSN 0974-9381

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Official URL: http://www.scientificadvances.co.in/artical/5/147

Abstract

This paper derives a new variable step 3-point block method based on Backward Differentiation Formula (BDF) for solving stiff Ordinary Differential Equations (ODEs). The strategy involved in the developed method is to control the step size at each iteration to optimize the precision and produce three solution values simultaneously at each step. The method is analyzed in having the conditions for zero stability and found to be of order 6. The stability regions of the method are also investigated and presented in distinct graphs. The proposed method is compared to MATLAB’s suite ODEs solvers, namely, ode15s and ode23s. Numerical results obtained are provided to support the enhancement of the method in terms of accuracy.

Item Type:Article
Keyword:Block; Backward differentiation formula; Stiff; Variable step size
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:Scientific Advances Publishers
ID Code:36199
Deposited By: Nabilah Mustapa
Deposited On:13 Jun 2015 09:32
Last Modified:24 Aug 2015 10:33

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