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Numerical solution of second-order one-dimensional hyperbolic equation by exponential B-spline collocation method

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Abstract

In this paper, we propose a method based on collocation of exponential B-splines to obtain numerical solution of a nonlinear second-order one-dimensional hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The method is a combination of B-spline collocation method in space and two-stage, second-order strong-stability-preserving Runge–Kutta method in time. The proposed method is shown to be unconditionally stable. The efficiency and accuracy of the method are successfully described by applying the method to a few test problems.

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Authors and Affiliations

  1. Department ofMathematics, Sri Venkateswara College, University of Delhi, New Delhi, 110021, India

    Swarn Singh

  2. Department of Mathematics, University of Delhi, New Delhi, 110007, India

    Suruchi Singh

  3. Department of Mathematics, Aditi Mahavidyalaya, University of Delhi, Delhi, 110039, India

    R. Arora

Authors
  1. Swarn Singh
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  2. Suruchi Singh
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  3. R. Arora
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Correspondence to Swarn Singh.

Additional information

Original Russian Text © Swarn Singh, Suruchi Singh, R. Arora, 2017, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2017, Vol. 20, No. 2, pp. 201–213.

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Singh, S., Singh, S. & Arora, R. Numerical solution of second-order one-dimensional hyperbolic equation by exponential B-spline collocation method. Numer. Analys. Appl. 10, 164–176 (2017). https://doi.org/10.1134/S1995423917020070

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  • DOI: https://doi.org/10.1134/S1995423917020070

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