Abstract
A comprehensive research on the existing Block Backward Differentiation Formulae (BBDF) was done. Based on the suitability in solving stiff ordinary differential equations (ODEs), BBDF of order 3 up 5 is collected using simplified strategy in controlling the step size and order of the method. Thus, Extended Block Backward Differentiation Formulae (EBBDF) is derived with the intention of optimizing the performance in terms of precision and computation time. The accuracy of the method are investigated using linear and non linear stiff initial value problems and its performance is compared with MATLAB’s suite of ODEs solvers namely ode15s and ode23s.
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Sack-Davis R (1980) Fixed leading coefficient implementation of SD-formulas for stiff ODEs. ACM Trans Math Softw 6(4):540–562
Yatim SAM, Ibrahim ZB, Othman KI, Suleiman MB (2011) Quantitative comparison of numerical method for solving stiff ordinary differential equations. Math Prob Eng 2011, ID 193961
Mahmood AS, Casasus L, Al-Hayani W (2005) The decomposition method for stiff systems of ordinary differential equations. Appl Math Comput 167(2):964–975
Ibanez J, Hernandez V, Arias E, Ruiz PA (2009) Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods. Comput Phys Commun 180(5):712–723
Enright WH, Hull TE, Lindberg B (1975) Comparing numerical methods for stiff systems of O.D.Es. BIT 15(1):10–48
Byrne GD, Hindmarsh AC, Jackson KR, Brown HG (1977) A comparison of two ode codes: gear and episode. Comput Chem Eng 1(2):133–147
Cash JR, Considine S (1992) An MEBDF code for stiff initial value problems. ACM Trans Math Softw 18(2):142–155
Abelman S, Patidar KC (2008) Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations. Comput Math Appl 55(4):733–744
Ibrahim ZB, Suleiman MB, Othman KI (2008) Fixed coefficients block backward differentiation formulas for the numerical solution of stiff ordinary differential equations. Eur J Sci Res 21(3):508–520
Ibrahim ZB, Othman KI, Suleiman MB (2007) Variable step size block backward differentiation formula for solving stiff odes. In: Proceedings of the world congress on engineering 2007, WCE 2007, London, UK, pp 785–789, 2–4 July 2007
Yatim SAM, Ibrahim ZB, Othman KI, Suleiman MB (2010) Fifth order variable step block backward differentiation formulae for solving stiff ODEs. Proc World Acad Sci Eng Tech 62:998–1000
Yatim SAM, Ibrahim ZB, Othman KI, Suleiman MB (2012) Numerical solution of extended block backward differentiation formulae for solving stiff ODEs, Lecture notes in engineering and computer science: proceedings of the world congress on engineering 2012, WCE 2012, London, UK, pp 109–113, 4–6 July 2012
Lambert JD (1973) Computational methods ordinary differential equation. Wiley, New York
Hall G, Watt JM (1976) Modern numerical methods for ordinary differential equations. Clarendon Press, Oxford
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Yatim, S.A.M., Ibrahim, Z.B., Othman, K.I., Suleiman, M. (2013). Solving Stiff Ordinary Differential Equations Using Extended Block Backward Differentiation Formulae. In: Yang, GC., Ao, Sl., Gelman, L. (eds) IAENG Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 229. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6190-2_3
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DOI: https://doi.org/10.1007/978-94-007-6190-2_3
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