The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory.
| Published in | Applied and Computational Mathematics (Volume 3, Issue 4) |
| DOI | 10.11648/j.acm.20140304.15 |
| Page(s) | 137-149 |
| 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), 2014. Published by Science Publishing Group |
Advection Diffusion Problem, Reciprocity, Integral Representation, Fundamental Solution, Generalization
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APA Style
H. Isshiki. (2014). Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem. Applied and Computational Mathematics, 3(4), 137-149. https://doi.org/10.11648/j.acm.20140304.15
ACS Style
H. Isshiki. Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem. Appl. Comput. Math. 2014, 3(4), 137-149. doi: 10.11648/j.acm.20140304.15
AMA Style
H. Isshiki. Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem. Appl Comput Math. 2014;3(4):137-149. doi: 10.11648/j.acm.20140304.15
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Download@article{10.11648/j.acm.20140304.15,
author = {H. Isshiki},
title = {Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem},
journal = {Applied and Computational Mathematics},
volume = {3},
number = {4},
pages = {137-149},
doi = {10.11648/j.acm.20140304.15},
url = {https://doi.org/10.11648/j.acm.20140304.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.15},
abstract = {The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory.},
year = {2014}
}
TY - JOUR T1 - Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem AU - H. Isshiki Y1 - 2014/08/10 PY - 2014 N1 - https://doi.org/10.11648/j.acm.20140304.15 DO - 10.11648/j.acm.20140304.15 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 137 EP - 149 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20140304.15 AB - The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory. VL - 3 IS - 4 ER -
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