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Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions

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Abstract

In this paper, the meshless local radial point interpolation (MLRPI) method is applied to the one-dimensional telegraph equation with purely integral conditions. In MLRPI, it does not require any background integration cells but it requires all integrations be carried out locally over small quadrature domains of regular shapes, such as lines in one dimension, circles or squares in two dimensions and spheres or cubes in three dimensions. A technique is proposed to construct shape functions using point interpolation method augmented to the radial basis functions. The time derivatives are approximated by the finite difference method. Some numerical experiments for the mentioned problem are carried out as well.

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, 34149-16818, Qazvin, Iran

    Elyas Shivanian & Hamid Reza Khodabandehlo

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  1. Elyas Shivanian
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  2. Hamid Reza Khodabandehlo
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Correspondence to Elyas Shivanian.

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Shivanian, E., Reza Khodabandehlo, H. Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions. Eur. Phys. J. Plus 129, 241 (2014). https://doi.org/10.1140/epjp/i2014-14241-9

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  • DOI: https://doi.org/10.1140/epjp/i2014-14241-9

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