A novel B-spline collocation method for Hyperbolic Telegraph equation

Emre Kırlı; Emre Kırlı

doi:10.3934/math.2023558

AIMS Mathematics

2023, Volume 8, Issue 5: 11015-11036. doi: 10.3934/math.2023558

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Research article

A novel B-spline collocation method for Hyperbolic Telegraph equation

Emre Kırlı ^,

Graduate School of Natural and Applied Sciences, Eskisehir Osmangazi University, Eskisehir 26040, Turkey

Received: 29 December 2022 Revised: 19 February 2023 Accepted: 22 February 2023 Published: 08 March 2023
MSC : 76B25, 65D07, 65M50, 65N35

The present study is concerned with the construction of a new high-order technique to establish approximate solutions of the Telegraph equation (TE). In this technique, a novel optimal B-spline collocation method based on quintic B-spline (QBS) basis functions is constructed to discretize the spatial domain and fourth-order implicit method is derived for time integration. Test problems are considered to verify the theoretical results and to demonstrate the applicability of the suggested technique. The error norm $ L_{\infty } $ and the rate of spatial and temporal convergence are computed and compared with those of techniques available in the literature. The obtained results show the improvement and efficiency of the proposed scheme over the existing ones. Also, it is obviously observed that the experimental rate of convergence is almost compatible with the theoretical rate of convergence.
- optimal quintic B-spline,
- Telegraph equation,
- collocation method
Citation: Emre Kırlı. A novel B-spline collocation method for Hyperbolic Telegraph equation[J]. AIMS Mathematics, 2023, 8(5): 11015-11036. doi: 10.3934/math.2023558

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Abstract

The present study is concerned with the construction of a new high-order technique to establish approximate solutions of the Telegraph equation (TE). In this technique, a novel optimal B-spline collocation method based on quintic B-spline (QBS) basis functions is constructed to discretize the spatial domain and fourth-order implicit method is derived for time integration. Test problems are considered to verify the theoretical results and to demonstrate the applicability of the suggested technique. The error norm $ L_{\infty } $ and the rate of spatial and temporal convergence are computed and compared with those of techniques available in the literature. The obtained results show the improvement and efficiency of the proposed scheme over the existing ones. Also, it is obviously observed that the experimental rate of convergence is almost compatible with the theoretical rate of convergence.

References

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