Share This Article:

A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

Full-Text HTML Download Download as PDF (Size:125KB) PP. 341-344
DOI: 10.4236/ajcm.2012.24047    4,091 Downloads   6,844 Views   Citations

ABSTRACT

We consider direct solution to third order ordinary differential equations in this paper. Method of collection and interpolation of the power series approximant of single variable is considered to derive a linear multistep method (LMM) with continuous coefficient. Block method was later adopted to generate the independent solution at selected grid points. The properties of the block viz: order, zero stability and stability region are investigated. Our method was tested on third order ordinary differential equation and found to give better result when compared with existing methods.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Adesanya, M. Udo and A. Alkali, "A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)," American Journal of Computational Mathematics, Vol. 2 No. 4, 2012, pp. 341-344. doi: 10.4236/ajcm.2012.24047.

References

[1] A. O. Adesanya and T. A. Udoh, “Improved Continuous Method for Direct Solution of General Second Order Ordinary Differential Equation,” Journal of Nigeria Association of Mathematical Physics, Vol. 13, 2008, pp. 59- 62.
[2] D. O. Awoyemi, “A P-Stable Linear Multistep Method for Solving Third Order Ordinary Differential Equation,” International Journal of Computer Mathematics, Vol. 80, No. 8, 2003, pp. 85-991. doi:10.1080/0020716031000079572
[3] D. O. Awoyemi and M. O. Idowu, “A Class of Hybrid Collocation Method for Third Order Ordinary Differential Equation,” International Journal of Computer Mathematics, Vol. 82, No. 10, 2005, pp. 1287-1293. doi:10.1080/00207160500112902
[4] S. N. Jator, “A Sixth Order Linear Multistep Method for Direct Solution of y’’=f(x,y,y’),” International Journal of Pure and Applied Mathematics, Vol. 40, No. 1, 2007, pp. 457-472.
[5] S. N. Jator and J. Li, “A Self Starting Linear Multistep Method for the Direct Solution of the General Second Order Initial Value Problems,” International Journal of Computer Mathematics, Vol. 86, No. 5, 2009, pp. 817- 836. doi:10.1080/00207160701708250
[6] D. O. Awoyemi, E. A. Adebile, A. O. Adesanya and T. A. Anake, “Modified Block Method for Direct Solution of Second Order Ordinary Differential Equation,” International Journal of Applies Mathematics and Computation, Vol. 3, No. 3, 2011, pp. 181-188.
[7] J. D. Lambert, “Computational Methods in Ordinary Differential Equation,” John Wiley & Sons Inc., Hoboken, 1973.
[8] S. O. Fatunla, M. N. O. Ikhile and F. O. Otunta, “A Class of P-Stable Linear Multistep Numerical Method,” International Journal of Computer Mathematics, Vol. 72, 1999, pp. 1-13. doi:10.1080/00207169908804830
[9] S. J. Kayode and D. O. Awoyemi, “A Multi-Derivative Collocation Method for Fifth Order Ordinary Differential Equation,” Journal of Mathematics and Statistics, Vol. 6, No. 1, 2010, pp. 60-63. doi:10.3844/jmssp.2010.60.63
[10] Z. Omar and M. Suleiman, “Parallel R-Point Implicit Block Method for Solving Higher Order Ordinary Differential Equation Directly,” Journal of ICT, Vol. 3, No. 1, 2003, pp. 53-66.
[11] L. F. Shampine and H. A. Watts, “Block Implicit One Step Methods,” Journal of Math of Computation, Vol. 23, No. 108, 1969, pp. 731-740. doi:10.1090/S0025-5718-1969-0264854-5
[12] S. J. Kayode, “A Zero Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations,” American Journal of Applied Sciences, Vol. 5, No. 11, 2009, pp. 1461-1466.
[13] B. T. Olabode and Y. Yusuf, “A New Block Method for Special Third Order Ordinary Differential Equation,” Journal of Mathematics and statistics, Vol. 5, No. 3, 2009, pp. 167-170.
[14] D. O. Awoyemi, M. O. Udoh and A. O. Adesanya, “Non-Symmetric Collocation Method for Direct Solution of General Third Order Initial Value Problems of Ordinary Differential Equation,” Journal of Natural and Applied Mathematics, Vol. 7, 2006, pp. 31-37.
[15] S. Abbas, “Derivation of a New Block Method Similar to the Block Trapezoidal Rule for the Numerical Solution of First Order IVP’s,” Science Echoes, Vol. 2, 2006, pp. 10-24.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.