Abstract:
In this paper, we propose a method based on collocation of exponential B-splines to obtain numerical solution of 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.
This publication is cited in the following 16 articles:
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O. E. Hepson, I. Dag, “An exponential cubic B-spline algorithm for solving the nonlinear coupled Burgers' equation”, Comput. Methods Differ. Equ., 9:4 (2021), 1109–1127
Singh S., Singh S., Aggarwal A., “Fourth-Order Cubic B-Spline Collocation Method For Hyperbolic Telegraph Equation”, Math. Sci., 2021
Brajesh Kumar Singh, Jai Prakash Shukla, Mukesh Gupta, “Study of One Dimensional Hyperbolic Telegraph Equation Via a Hybrid Cubic B-Spline Differential Quadrature Method”, Int. J. Appl. Comput. Math, 7:1 (2021)
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B. Ch. Park, “Author's reply to the comment on: “the effect of intradermal botulinum toxin on androgenetic alopecia and its possible mechanism””, J. Am. Acad. Dermatol., 83:6 (2020), E437
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I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Generalized spline interpolation of functions with large gradients in boundary layers”, Comput. Math. Math. Phys., 60:3 (2020), 411–426
S. Singh, S. Singh, R. Arora, “An unconditionally stable numerical method for two-dimensional hyperbolic equations”, East Asian J. Appl. Math., 9:1 (2019), 195–211
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