Applied and Computational Mathematics

Volume 4, Issue 3, June 2015

  • From Integral Representation Method (IRM) to Generalized Integral Representation Method (GIRM)

    Hiroshi Isshiki

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 1-14
    Received: 26 December 2014
    Accepted: 30 December 2014
    Published: 12 February 2015
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    This article belongs to the Special Issue Integral Representation Method and its Generalization
    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. However, it was originally developed for linear equations with known fundamental solutions. In order to apply to general nonlinear equations, we must gen... Show More
  • Application of Generalized Integral Representation (GIRM) Method to Fluid Dynamic Motion of Gas or Particles in Cosmic Space Driven by Gravitational Force

    Hiroshi Isshiki, Toshio Takiya, Hideyuki Niizato

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 15-39
    Received: 22 December 2014
    Accepted: 25 December 2014
    Published: 12 February 2015
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    This article belongs to the Special Issue Integral Representation Method and its Generalization
    Abstract: Some aspect of the motion of gas or vast-number-of-particles distributed in cosmic space under action of the gravitational force may be treated as a fluid dynamic motion without pressure. Generalized Integral representation Method (GIRM) is applied to fluid dynamic motion of gas or particles to obtain the accurate numerical solutions. In the presen... Show More
  • Effects of Generalized Fundamental Solution (GFS) on Generalized Integral Representation Method (GIRM)

    Hiroshi Isshiki

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 40-51
    Received: 05 February 2015
    Accepted: 06 February 2015
    Published: 13 March 2015
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    This article belongs to the Special Issue Integral Representation Method and its Generalization
    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 F... Show More
  • Application of the Generalized Integral Representation Method (GIRM) to Tidal Wave Propagation

    Hiroshi Isshiki

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 52-58
    Received: 25 February 2015
    Accepted: 25 February 2015
    Published: 26 March 2015
    Downloads:
    Views:
    This article belongs to the Special Issue Integral Representation Method and its Generalization
    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 F... Show More
  • Implementation of One and Two-Step Generalized Integral Representation Methods (GIRMs)

    Hideyuki Niizato, Gantulga Tsedendorj, Hiroshi Isshiki

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 59-77
    Received: 19 March 2015
    Accepted: 23 March 2015
    Published: 08 April 2015
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    This article belongs to the Special Issue Integral Representation Method and its Generalization
    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 ... Show More
  • Application of Generalized Integral Method (GIRM) to Numerical Evaluations of Soliton-to-Soliton and Soliton-to-Bottom Interactions

    Gantulga Tsedendorj, Hiroshi Isshiki, Rinchinbazar Ravsal

    Issue: Volume 4, Issue 3-1, June 2015
    Pages: 78-86
    Received: 17 April 2015
    Accepted: 17 April 2015
    Published: 12 May 2015
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    This article belongs to the Special Issue Integral Representation Method and its Generalization
    Abstract: Numerical evaluations of soliton-soliton and soliton-to-bottom interaction have many applications in various fields. On the other hand, Generalized Integral Representation Method (GIRM) is known as a convenient numerical method for solving Initial and Boundary Value Problem of differential equations such as advective diffusion. In this work, we app... Show More