Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM)
Applied and Computational Mathematics
Volume 4, Issue 3-1, June 2015, Pages: 40-51
Received: Feb. 5, 2015; Accepted: Feb. 6, 2015; Published: Mar. 13, 2015
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Author
Hiroshi Isshiki, IMA, Institute of Mathematical Analysis, Osaka, Japan
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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. IRM is developed to Generalized Integral Representation Method (GIRM) to treat any kinds of problems including nonlinear problems. In GIRM, Generalized Fundamental Solution (GFS) is used instead of Fundamental Solution (FS) in IRM. Since GFS is not limited to one, the effects of individual GFSs must be clarified. The continuity of GFS is related to the characteristics of individual GFSs.
Keywords
Initial and Boundary Value Problems (IBVP), Integral Representation Method (IRM), Generalized Integral Representation Method (GIRM), Generalized Fundamental Solution (GFS)
To cite this article
Hiroshi 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. Vol. 4, No. 3-1, 2015, pp. 40-51. doi: 10.11648/j.acm.s.2015040301.13
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