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A collocation approach for solving two-dimensional second-order linear hyperbolic equations

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  • Yüzbaşı, Şuayip

Abstract

In this study, a collocation approach is introduced to solve second-order two-dimensional hyperbolic telegraph equation under the initial and boundary conditions. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. The method is constructed in four steps for the considered problem. In first step we construct the fundamental relations for the solution method. By using the collocation points and matrix operations, second step gives the constructing of the main matrix equation. In third step, matrix forms are created for the initial and boundary conditions. We compute the approximate solutions by combining second and third steps. Algorithm of the proposed method is given. Later, error estimation technique is presented and the approximate solutions are improved. Numerical applications are included to demonstrate the validity and applicability of the presented method.

Suggested Citation

  • Yüzbaşı, Şuayip, 2018. "A collocation approach for solving two-dimensional second-order linear hyperbolic equations," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 101-114.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:101-114
    DOI: 10.1016/j.amc.2018.05.053
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2007. "The one-dimensional heat equation subject to a boundary integral specification," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 661-675.
    2. Zhang, Baowen & Ma, Hailong, 2016. "A meshless collocation approach with barycentric rational interpolation for two-dimensional hyperbolic telegraph equationAuthor-Name: Ma, Wentao," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 236-248.
    3. B. Pekmen & M. Tezer-Sezgin, 2012. "Differential Quadrature Solution of Hyperbolic Telegraph Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, July.
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