Oluwaseun ADEYEYE, Zurni OMAR

Computational Complexity Comparison of a New Linear Block Approach and Modified Taylor Series Approach for Developing k-Step Third Derivative Block Methods

Yayın Aralığı: 4
Başlangıç: 1988
Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü

This article introduces two approaches to develop block methods for solving second orderordinary differential equations directly. Both approaches, namely a new linear block approachand the modified Taylor series approach are capable of producing a family of methods that willsimultaneously approximate the solutions of any ordinary differential equation at the respectivegrid points of the block method. The computational complexities of both approaches areexamined, and the results show the new linear block approach require less computationscompared to the modified Taylor series approach.

PDF

___

Awoyemi, D. O., “A new sixth-order algorithm for general second order ordinary differential equations”, International Journal of Computer Mathematics, 77(1): 117-124, (2001).
Butcher, J. C., “Numerical methods for ordinary differential equations”, Wiley, West Sussex, (2008).
Fatunla, S. O., “Numerical methods for initial value problems in ordinary differential equations”, Academic Press, New York, (1988).
Lambert, J. D., “Computational methods in ordinary differential equations”, Wiley, (1973)
Omar, Z., Kuboye, J. O., “Derivation of block methods for solving second order ordinary differential equations directly using direct integration and collocation approaches”, Indian Journal of Science and Technology, 8(12): 1-4, (2015).
Awoyemi, D. O., Kayode, S. J., “A maximal order collocation method for direct solution of initial value problems of general second order ordinary differential equations”, In Proceedings of the conference organized by the National Mathematical Centre, Abuja, Nigeria, (2005).
Jator, S. N., Swindel, S, French, R., “Trigonometrically fitted block Numerov type method for y f x y y '' , , '    ”, Numerical Algorithms, 62(1): 13-26, (2013).