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

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

This article introduces two approaches to develop block methods for solving second order ordinary differential equations directly. Both approaches, namely a new linear block approach and the modified Taylor series approach are capable of producing a family of methods that will simultaneously approximate the solutions of any ordinary differential equation at the respective grid points of the block method. The computational complexities of both approaches are examined, and the results show the new linear block approach require less computations compared to the modified Taylor series approach.

Keywords:

Computational Complexity, New Linear Block, Modified Taylor Series Block Methods, Second Order ODEs,

PDF

___

Awoyemi D O. A new sixth-order algorithm for general second order ordinary differential equations. Int. J. of Comp. Math., 2001, 77(1): 117-124.
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.
Butcher J C. Numerical methods for ordinary differential equations. 2008, West Sussex: Wiley.
Fatunla S O. Numerical methods for initial value problems in ordinary differential equations. 1988, New York: Academic Press.
Jator S N, Swindel, S, French R. Trigonometrically fitted block Numerov type method for y''=f(x,y,y') Num. Algor., 2013, 62(1): 13-26.
Lambert J D, Computational methods in ordinary differential equations. 1973, Wiley.
Omar Z, Kuboye, J O. Derivation of Block Methods for Solving Second Order Ordinary Differential Equations Directly using Direct Integration and Collocation Approaches. Indian J. of Sci. and Tech., 2015, 8(12): 1-4.