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Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs)
Applied and Computational Mathematics
Volume 4, Issue 3-1, June 2015, Pages: 59-77
Received: Mar. 19, 2015; Accepted: Mar. 23, 2015; Published: Apr. 8, 2015
Authors
Hideyuki Niizato, Hitachi Zosen Corporation, Osaka, Japan
Gantulga Tsedendorj, Department of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
Hiroshi Isshiki, IMA, Institute of Mathematical Analysis, Osaka, Japan
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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.
Keywords
Initial and Boundary Value Problem (IBVP), Generalized Fundamental Solution, Generalized Integral Representation Method (GIRM), Implementation of GIRM, Computer Codes
Hideyuki Niizato, Gantulga Tsedendorj, Hiroshi Isshiki, Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs), Applied and Computational Mathematics. Special Issue: Integral Representation Method and its Generalization. Vol. 4, No. 3-1, 2015, pp. 59-77. doi: 10.11648/j.acm.s.2015040301.15
References
[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
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