Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations

Kamoh Nathaniel Mahwash; Awari Yohanna Sani; Chun Pamson Bentse

doi:doi:10.11648/j.ijdst.20170304.11

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Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations

Kamoh Nathaniel Mahwash, Awari Yohanna Sani, Chun Pamson Bentse

Published in International Journal on Data Science and Technology (Volume 3, Issue 4)

Received: 1 June 2017 Accepted: 21 August 2017 Published: 26 September 2017

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Abstract

This paper presents the derivation techniques of block method for solving higher order initial value problems of ordinary differential equations directly. The method was developed via interpolation and collocation of the shifted Legendre polynomials as basis function. The method is capable of providing the numerical solution at several points simultaneously.

Published in	International Journal on Data Science and Technology (Volume 3, Issue 4)
DOI	10.11648/j.ijdst.20170304.11
Page(s)	39-44
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Collocation, Interpolation, Shifted Legendre Polynomials, Block Method, Higher Order, Direct Solution, Initial Value Problems

References

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[3]	Anake, T. A. (2011). Continuous Implicit Hybrid One –Step Methods for the Solution of Initial Value Problems of Second Order Ordinary Differential Equations. PhD Thesis, Covenant University, Ota, Ogun State, Nigeria.
[4]	Awarri, Y. S., Chima, E. E., Kamoh, N. M. and Oladele, F. L. (2014). A Family of Implicit Uniformly Accurate Order Block Integrators for the Solution of Second Order Differential Equations; International Journal of Mathematics and Statistics Invention (IJMSI).2: 34-46.
[5]	Areo, E. A., Ademiluyi, R. A. and Babatola, P. O. (2008). Accurate Collocation Multistep Method for integration of first order ordinary differential equations. Journal of Modern Mathematics and Statistics. 2(1): 1-6.
[6]	Awoyemi, D. O. (1991). A Class of Continuous Linear Multistep Method for General Second Order Initial Value Problems in Ordinary Differential Equations. International Journal of Computer Mathematics.72: 29-37.
[7]	Awoyemi, D. O and Kayode, S. J. (2005). An Implicit Collocation Method for Direct Solution of Second Order Ordinary Differential Equations; Journal of Nigeria Association of Mathematical Physics.24:70-78.
[8]	Awoyemi, D. O. (2001). A New Sixth-Order Algorithm for General Second Order Ordinary Differential Equation. International Journal of computational mathematics. 77: 117-124.
[9]	Serisina, U. W., Kumleng, G. M. and Yahaya, Y. A. (2004). A New Butcher Type Two-Step Block Hybrid Multistep Method for Accurate and Efficient Parallel Solution of Ordinary Differential Equations. Abacus Mathematics Series31:1-7.
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APA Style

Kamoh Nathaniel Mahwash, Awari Yohanna Sani, Chun Pamson Bentse. (2017). Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. International Journal on Data Science and Technology, 3(4), 39-44. https://doi.org/10.11648/j.ijdst.20170304.11

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ACS Style

Kamoh Nathaniel Mahwash; Awari Yohanna Sani; Chun Pamson Bentse. Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. Int. J. Data Sci. Technol. 2017, 3(4), 39-44. doi: 10.11648/j.ijdst.20170304.11

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AMA Style

Kamoh Nathaniel Mahwash, Awari Yohanna Sani, Chun Pamson Bentse. Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. Int J Data Sci Technol. 2017;3(4):39-44. doi: 10.11648/j.ijdst.20170304.11

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@article{10.11648/j.ijdst.20170304.11,
  author = {Kamoh Nathaniel Mahwash and Awari Yohanna Sani and Chun Pamson Bentse},
  title = {Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations},
  journal = {International Journal on Data Science and Technology},
  volume = {3},
  number = {4},
  pages = {39-44},
  doi = {10.11648/j.ijdst.20170304.11},
  url = {https://doi.org/10.11648/j.ijdst.20170304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20170304.11},
  abstract = {This paper presents the derivation techniques of block method for solving higher order initial value problems of ordinary differential equations directly. The method was developed via interpolation and collocation of the shifted Legendre polynomials as basis function. The method is capable of providing the numerical solution at several points simultaneously.},
 year = {2017}
}

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TY  - JOUR
T1  - Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations
AU  - Kamoh Nathaniel Mahwash
AU  - Awari Yohanna Sani
AU  - Chun Pamson Bentse
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdst.20170304.11
DO  - 10.11648/j.ijdst.20170304.11
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 39
EP  - 44
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20170304.11
AB  - This paper presents the derivation techniques of block method for solving higher order initial value problems of ordinary differential equations directly. The method was developed via interpolation and collocation of the shifted Legendre polynomials as basis function. The method is capable of providing the numerical solution at several points simultaneously.
VL  - 3
IS  - 4
ER  -

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Author Information

Kamoh Nathaniel Mahwash

Department of Mathematics/Statistics Bingham University, Karu, Nigeria
Awari Yohanna Sani

Department of Mathematics/Statistics Bingham University, Karu, Nigeria
Chun Pamson Bentse

Department of Mathematics/Statistics Plateau State University Bokkos, Bokkos, Nigeria

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APA Style

Kamoh Nathaniel Mahwash, Awari Yohanna Sani, Chun Pamson Bentse. (2017). Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. International Journal on Data Science and Technology, 3(4), 39-44. https://doi.org/10.11648/j.ijdst.20170304.11

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ACS Style

Kamoh Nathaniel Mahwash; Awari Yohanna Sani; Chun Pamson Bentse. Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. Int. J. Data Sci. Technol. 2017, 3(4), 39-44. doi: 10.11648/j.ijdst.20170304.11

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AMA Style

Kamoh Nathaniel Mahwash, Awari Yohanna Sani, Chun Pamson Bentse. Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations. Int J Data Sci Technol. 2017;3(4):39-44. doi: 10.11648/j.ijdst.20170304.11

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@article{10.11648/j.ijdst.20170304.11,
  author = {Kamoh Nathaniel Mahwash and Awari Yohanna Sani and Chun Pamson Bentse},
  title = {Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations},
  journal = {International Journal on Data Science and Technology},
  volume = {3},
  number = {4},
  pages = {39-44},
  doi = {10.11648/j.ijdst.20170304.11},
  url = {https://doi.org/10.11648/j.ijdst.20170304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20170304.11},
  abstract = {This paper presents the derivation techniques of block method for solving higher order initial value problems of ordinary differential equations directly. The method was developed via interpolation and collocation of the shifted Legendre polynomials as basis function. The method is capable of providing the numerical solution at several points simultaneously.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Collocation Techniques for Block Methods for the Direct Solution of Higher Order Initial Value Problems of Ordinary Differential Equations
AU  - Kamoh Nathaniel Mahwash
AU  - Awari Yohanna Sani
AU  - Chun Pamson Bentse
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdst.20170304.11
DO  - 10.11648/j.ijdst.20170304.11
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 39
EP  - 44
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20170304.11
AB  - This paper presents the derivation techniques of block method for solving higher order initial value problems of ordinary differential equations directly. The method was developed via interpolation and collocation of the shifted Legendre polynomials as basis function. The method is capable of providing the numerical solution at several points simultaneously.
VL  - 3
IS  - 4
ER  -

Copy | Download