A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations

Kaze Atsi*, Lydia Adiku**, Namuma Yarima***, G. M. Kumleng****
* Department of Mathematics, Federal University Gashua, Yobe State, Nigeria.
**-*** Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
**** Department of Mathematics, University of Jos, Plateau State, Nigeria.
Periodicity:July - December'2022
DOI : https://doi.org/10.26634/jmat.11.2.19206

Abstract

In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.

Keywords

Second Derivative, BDF, Block Methods, Stiff Ordinary Differential Equations (SODEs), Stability.

How to Cite this Article?

Atsi, K., Adiku, L., Yarima, N., and Kumleng, G. M. (2022). A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations. i-manager’s Journal on Mathematics, 11(2), 8-12. https://doi.org/10.26634/jmat.11.2.19206

References

[1]. Ajie, I. J., Ikhile, M. N. O., & Onumanyi, P. (2014). A family of block methods derived from TOM and BDF pairs for stiff ordinary differential equations. American Journal of Mathematics and Statistics, 4(2), 121-130. https://doi.org/10.5923/j.ajms.20140402.08
[2]. Akinfenwa, O. A., Jator, S. N., & Yao, N. M. (2012). On the stability of continuous block backward differentiation formula for solving stiff ordinary differential equations. Journal of Modern Methods in Numerical Mathematics, 3(2), 50-58. https://doi.org/10.20454/jmmnm.2012.321
[3]. Atsi, K., & Kumleng, G. M. (2020). A family of modified backward differentiation formula (BDF) type block methods for the solution of stiff ordinary differential equations. International Journal of Statistics and Applied Mathematics, 5(2), 09-16.
[4]. Atsi, K., & Kumleng, G. M. (2021). Block extended trapezoidal rule of the second kind (Etr2) for the direct soltion of second order initial value problems of ordinary differential equations. IOSR Journal of Mathematics (IOSR-JM), 17(2), 10-14. https://doi.org/10.9790/5728-1702041014
[5]. Atsi, K., Hambagda, B., Ogunwuyi, F. E., & Kumleng, G. M. (2021). A block integrator for the solution of first order ordinary differential equations using legendre polynomial. Asian Journal of Pure and Applied Mathematics, 3(2) 1-7.
[6]. Chollom, J. P., Ndam, J. N., & Kumleng, G. M. (2007). On some properties of the block linear multi-step methods. Science World Journal, 2(3), 11-17. https://doi.org/10.4314/swj.v2i3.51747
[7]. Kumleng, G. M., Chollom, J. P., & Longwap, S. (2013). A modified block adam moulton (MOBAM) method for the solution of stiff initial value problems of ordinary differential equations. Research Journal of Mathematics and Statistics, 5(4), 32-42.
[8]. Kumleng, G. M., Chollom, J. P., & Omagwu, S. (2015). A class of new block generalized adams implicit runge-kutta collocation methods. International Journal of Scientific & Engineering Research, 6(12), 10-19.
[9]. Kumleng, G. M., Longwap, S., & Adee, S. O. (2013). A class of a-stable order four and six linear multistep methods for stiff initial value problems. Mathematical Theory and Modeling, 3(11), 1-9.
[10]. Skwame, Y., Sunday, J., & Ibijola, E. A. (2012). L-stable block hybrid simpson's methods for numerical solution of initial value problems in stiff ordinary differential equations. International Journal of Pure and Applied Sciences and Technology, 11(2), 45-54.
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