In this study, we summarize and implement one- and two-step Generalized Integral Representation Methods (GIRMs). Although GIRM requires matrix inversion, the solution is stable and the accuracy is high. Moreover, it can be applied to an irregular mesh. In order to validate the theory, we apply one- and two-step GIRMs to the one-dimensional Initial and Boundary Value Problem for advective diffusion. The numerical experiments are conducted and the approximate solutions coincide with the exact ones in both cases. The corresponding computer codes implemented in most popular computational languages 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.2015040301.15 |
| Page(s) | 59-77 |
| 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 |
Initial and Boundary Value Problem (IBVP), Generalized Fundamental Solution, Generalized Integral Representation Method (GIRM), Implementation of GIRM, Computer Codes
| [1] | H. Isshiki, “From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM),” Applied and Computational Mathematics, Special Issue: Integral Representation Method and Its Generalization, (2015), under publication. http://www.sciencepublishinggroup.com/ journal/archive.aspx?journalid=147&issueid=-1 |
| [2] | 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 publication. http://www.sciencepublishinggroup.com/journal/archive.aspx?journalid=147&issueid=-1 |
| [3] | H. Isshiki, “Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM),” Applied and Computational Mathematics, Special Issue: Integral Representation Method and Its Generalization, (2015), under publication. http://www.sciencepublishinggro up .com/journal/archive.aspx?journalid=147&issueid=-1 |
| [4] | H. Isshiki, “Application of the Generalized Integral Representation Method (GIRM) to Tidal Wave Propagation,” Applied and Computational Mathematics, Special Issue: Integral Representation Method and Its Generalization, (2015), under publication. http://www.sciencepublishinggroup.com/ journal/archive.aspx?journalid=147&issueid=-1 |
APA Style
Hideyuki Niizato, Gantulga Tsedendorj, Hiroshi Isshiki. (2015). Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs). Applied and Computational Mathematics, 4(3-1), 59-77. https://doi.org/10.11648/j.acm.s.2015040301.15
ACS Style
Hideyuki Niizato; Gantulga Tsedendorj; Hiroshi Isshiki. Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs). Appl. Comput. Math. 2015, 4(3-1), 59-77. doi: 10.11648/j.acm.s.2015040301.15
AMA Style
Hideyuki Niizato, Gantulga Tsedendorj, Hiroshi Isshiki. Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs). Appl Comput Math. 2015;4(3-1):59-77. doi: 10.11648/j.acm.s.2015040301.15
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Download@article{10.11648/j.acm.s.2015040301.15,
author = {Hideyuki Niizato and Gantulga Tsedendorj and Hiroshi Isshiki},
title = {Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs)},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {3-1},
pages = {59-77},
doi = {10.11648/j.acm.s.2015040301.15},
url = {https://doi.org/10.11648/j.acm.s.2015040301.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040301.15},
abstract = {In this study, we summarize and implement one- and two-step Generalized Integral Representation Methods (GIRMs). Although GIRM requires matrix inversion, the solution is stable and the accuracy is high. Moreover, it can be applied to an irregular mesh. In order to validate the theory, we apply one- and two-step GIRMs to the one-dimensional Initial and Boundary Value Problem for advective diffusion. The numerical experiments are conducted and the approximate solutions coincide with the exact ones in both cases. The corresponding computer codes implemented in most popular computational languages are also given.},
year = {2015}
}
TY - JOUR T1 - Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs) AU - Hideyuki Niizato AU - Gantulga Tsedendorj AU - Hiroshi Isshiki Y1 - 2015/04/08 PY - 2015 N1 - https://doi.org/10.11648/j.acm.s.2015040301.15 DO - 10.11648/j.acm.s.2015040301.15 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 59 EP - 77 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2015040301.15 AB - In this study, we summarize and implement one- and two-step Generalized Integral Representation Methods (GIRMs). Although GIRM requires matrix inversion, the solution is stable and the accuracy is high. Moreover, it can be applied to an irregular mesh. In order to validate the theory, we apply one- and two-step GIRMs to the one-dimensional Initial and Boundary Value Problem for advective diffusion. The numerical experiments are conducted and the approximate solutions coincide with the exact ones in both cases. The corresponding computer codes implemented in most popular computational languages are also given. VL - 4 IS - 3-1 ER -
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