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An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation

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Abstract

In this paper, a proficient numerical technique for the time-fractional telegraph equation (TFTE) is proposed. The chief aim of this paper is to utilize a relatively new type of B-spline called the cubic trigonometric B-spline for the proposed scheme. This technique is based on finite difference formulation for the Caputo time-fractional derivative and cubic trigonometric B-splines based technique for the derivatives in space. A stability analysis of the scheme is presented to confirm that the errors do not amplify. A convergence analysis is also presented. Computational experiments are carried out in addition to verify the theoretical analysis. Numerical results are contrasted with a few present techniques and it is concluded that the presented scheme is progressively right and more compelling.

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Authors and Affiliations

  1. Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan

    Muhammad Yaseen & Muhammad Abbas

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  1. Muhammad Yaseen
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  2. Muhammad Abbas
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Correspondence to Muhammad Abbas.

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Yaseen, M., Abbas, M. An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation. Appl. Math. J. Chin. Univ. 35, 359–378 (2020). https://doi.org/10.1007/s11766-020-3883-y

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  • DOI: https://doi.org/10.1007/s11766-020-3883-y

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