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Tension spline solution of nonlinear sine-Gordon equation

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Abstract

The sine-Gordon equation plays an important role in modern physics. By using spline function approximation, two implicit finite difference schemes are developed for the numerical solution of one-dimensional sine-Gordon equation. Stability analysis of the method has been given. It has been shown that by choosing the parameters suitably, we can obtain two schemes of orders \(\mathcal{O}(k^{2}+k^{2}h^{2}+h^{2})\) and \(\mathcal{O}(k^{2}+k^{2}h^{2}+h^{4})\). At the end, some numerical examples are provided to demonstrate the effectiveness of the proposed schemes.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, 1684613114, Tehran, Iran

    Jalil Rashidinia & Reza Mohammadi

  2. Department of Mathematics, University of Neyshabour, P.O. Box 899, Neyshabour, Iran

    Reza Mohammadi

Authors
  1. Jalil Rashidinia
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  2. Reza Mohammadi
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Correspondence to Jalil Rashidinia.

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Rashidinia, J., Mohammadi, R. Tension spline solution of nonlinear sine-Gordon equation. Numer Algor 56, 129–142 (2011). https://doi.org/10.1007/s11075-010-9377-x

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  • DOI: https://doi.org/10.1007/s11075-010-9377-x

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