From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)

Hiroshi Isshiki

doi:doi:10.11648/j.acm.s.2015040301.11

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From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)

Hiroshi Isshiki

Published in Applied and Computational Mathematics (Volume 4, Issue 3-1)

Received: 26 December 2014 Accepted: 30 December 2014 Published: 12 February 2015

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Abstract

Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given.

Published in	Applied and Computational Mathematics (Volume 4, Issue 3-1) This article belongs to the Special Issue Integral Representation Method and its Generalization
DOI	10.11648/j.acm.s.2015040301.11
Page(s)	1-14
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), 2015. Published by Science Publishing Group

Keywords

Initial and Boundary Value Problems (IBVP), Integral Representation Method (IRM), Generalized Integral Representation Method (GIRM), Generalized Fundamental Solution

References

[1]	Wu J.C., Thompson J.F., “Numerical solutions of time-dependent incompressible Navier-Stokes equations using an integro-differential formulations”, Computers & Fluids, (1973), 1, pp. 197-215.
[2]	S. J. Uhlman, “An integral equation formulation of the equations of motion of an incompressible fluid”, NUWC-NPT Technical Report 10,086, 15 July, (1992).
[3]	H. Isshik, S. Nagata, Y. Imai, “Solution of Viscous Flow around a Circular Cylinder by a New Integral Representation Method (NIRM)”, AJET, 2, 2, (2014), pp. 60-82. file:///C:/Users/l/Downloads/983-5001-1-PB%20(1).pdf
[4]	H. Isshik, S. Nagata, Y. Imai, “Solution of a diffusion problem in a non-homogeneous flow and diffusion field by the integral representation method (IRM)”, Applied and Computational Mathematics, 3(1), (2014), pp. 15-26. http://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140301.13.pdf
[5]	H. Isshiki, Theory and application of the generalized integral representation method (GIRM) in advection diffusion problem, Applied and Computational Mathematics, 3(4), (2014), pp. 137-149. http://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.15.pdf
[6]	H. Isshiki, T, Takiya and H. Niizato, Application of Generalized Integral representation (GIRM) Method to Fluid Dynamic Motion of Gas or Particles in Cosmic Space Driven by Gravitational Force, Applied and Computational Mathematics, Special Issue: Integral Representation Method and Its Generalization, (2015), under publicaion. http://www.sciencepublishinggroup.com/journal/archive.aspx?journalid=147&issueid=-1
[7]	H. Isshiki, A method for Reduction of Spurious or Numerical Oscillations in Integration of Unsteady Boundary Value Problem, AJET, 2, 3, (2014), pp. 190-202. file:///C:/Users/l/Downloads/1360-5725-2-PB%20(2).pdf
[8]	H. Isshiki, “Improvement of Stability and Accuracy of Time-Evolution Equation by Implicit Integration”, Asian Journal of Engineering and Technology (AJET), Vol. 2, No. 2 (2014), pp. 1339–160. file:///C:/Users/l/Downloads/1205-5161-1-PB.pdf

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Hiroshi Isshiki. (2015). From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Applied and Computational Mathematics, 4(3-1), 1-14. https://doi.org/10.11648/j.acm.s.2015040301.11

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ACS Style

Hiroshi Isshiki. From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Appl. Comput. Math. 2015, 4(3-1), 1-14. doi: 10.11648/j.acm.s.2015040301.11

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AMA Style

Hiroshi Isshiki. From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Appl Comput Math. 2015;4(3-1):1-14. doi: 10.11648/j.acm.s.2015040301.11

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@article{10.11648/j.acm.s.2015040301.11,
  author = {Hiroshi Isshiki},
  title = {From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3-1},
  pages = {1-14},
  doi = {10.11648/j.acm.s.2015040301.11},
  url = {https://doi.org/10.11648/j.acm.s.2015040301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040301.11},
  abstract = {Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given.},
 year = {2015}
}

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TY  - JOUR
T1  - From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)
AU  - Hiroshi Isshiki
Y1  - 2015/02/12
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.s.2015040301.11
DO  - 10.11648/j.acm.s.2015040301.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 14
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.s.2015040301.11
AB  - Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given.
VL  - 4
IS  - 3-1
ER  -

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Author Information

Hiroshi Isshiki

IMA, Institute of Mathematical Analysis, Osaka, Japan

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APA Style

Hiroshi Isshiki. (2015). From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Applied and Computational Mathematics, 4(3-1), 1-14. https://doi.org/10.11648/j.acm.s.2015040301.11

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ACS Style

Hiroshi Isshiki. From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Appl. Comput. Math. 2015, 4(3-1), 1-14. doi: 10.11648/j.acm.s.2015040301.11

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AMA Style

Hiroshi Isshiki. From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM). Appl Comput Math. 2015;4(3-1):1-14. doi: 10.11648/j.acm.s.2015040301.11

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@article{10.11648/j.acm.s.2015040301.11,
  author = {Hiroshi Isshiki},
  title = {From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3-1},
  pages = {1-14},
  doi = {10.11648/j.acm.s.2015040301.11},
  url = {https://doi.org/10.11648/j.acm.s.2015040301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040301.11},
  abstract = {Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)
AU  - Hiroshi Isshiki
Y1  - 2015/02/12
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.s.2015040301.11
DO  - 10.11648/j.acm.s.2015040301.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 14
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.s.2015040301.11
AB  - Integral Representation Method (IRM) is one of convenient methods to solve Initial and Boundary Value Problems (IBVP). It can be applied to irregular mesh, and the solution is stable and accurate. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must generalize the method. In the present paper, a generalization of IRM (GIRM) is discussed and applied to specific problems and the numerical solutions obtained. The numerical results are stable and accurate. The generalized method is called Generalized Integral Representation Method (GIRM). Brief explanations on the relationships with other numerical methods are also given.
VL  - 4
IS  - 3-1
ER  -

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