From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)
Applied and Computational Mathematics
Volume 4, Issue 3-1, June 2015, Pages: 1-14
Received: Dec. 26, 2014;
Accepted: Dec. 30, 2014;
Published: Feb. 12, 2015
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Hiroshi Isshiki, IMA, Institute of Mathematical Analysis, Osaka, Japan
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.
From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM), Applied and Computational Mathematics. Special Issue: Integral Representation Method and its Generalization.
Vol. 4, No. 3-1,
2015, pp. 1-14.
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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
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