A new trigonometric spline approach to numerical solution of generalized nonlinear Klien-Gordon equation
The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite...
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| Veröffentlicht in: | PloS one 2014-05, Vol.9 (5), p.e95774-e95774 |
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| description | The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and L∞ error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature. |
| doi_str_mv | 10.1371/journal.pone.0095774 |
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In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and L∞ error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature.</description><identifier>ISSN: 1932-6203</identifier><identifier>EISSN: 1932-6203</identifier><identifier>DOI: 10.1371/journal.pone.0095774</identifier><identifier>PMID: 24796483</identifier><language>eng</language><publisher>United States: Public Library of Science</publisher><subject>Applied mathematics ; Boundary conditions ; Boundary value problems ; Computational physics ; Computer and Information Sciences ; Dirichlet problem ; Feasibility studies ; Finite volume method ; Fractals ; Models, Theoretical ; Norms ; Partial differential equations ; Physical Sciences ; Problems ; Quantum mechanics</subject><ispartof>PloS one, 2014-05, Vol.9 (5), p.e95774-e95774</ispartof><rights>COPYRIGHT 2014 Public Library of Science</rights><rights>2014 Mat Zin et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 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In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. 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| subjects | Applied mathematics Boundary conditions Boundary value problems Computational physics Computer and Information Sciences Dirichlet problem Feasibility studies Finite volume method Fractals Models, Theoretical Norms Partial differential equations Physical Sciences Problems Quantum mechanics |
| title | A new trigonometric spline approach to numerical solution of generalized nonlinear Klien-Gordon equation |
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