Article
An Extended Theoretical and Numerical Study of two-Point Boundary Value Problems Using Collocation Method with Physical Applications
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Abstract
In this paper, we present a collocation method based on trigonometric quintic B-spline function is studied and applied for the numerical solutions of two-point boundary value problems arising in physical applications. The convergence of the trigonometric quintic B-spline collocation method is proved using diagonally dominant matrices. The numerical applications appear that our method is highly efficient and the maximum absolute error is convenient.
Keywords
Collocation method, Trigonometric quintic B-spline function, Two-point boundary value problems
Citation
Ali, K. K., Shaalan, M. A., & Raslan, K. R. (2019). An extended theoretical and numerical study of two-point boundary value problems using collocation method with physical applications. Numerical and Computational Methods in Sciences and Engineering, 1(1), 33–39. https://doi.org/10.18576/ncmsel/010104
K. K. Ali, M. A. Shaalan and K. R. Raslan, “An extended theoretical and numerical study of two-point boundary value problems using collocation method with physical applications,” Numerical and Computational Methods in Sciences and Engineering, vol. 1, no. 1, pp. 33–39, 2019, doi: 10.18576/ncmsel/010104.
Ali KK, Shaalan MA, Raslan KR. An extended theoretical and numerical study of two-point boundary value problems using collocation method with physical applications. Numerical and Computational Methods in Sciences and Engineering. 2019;1(1):33–39. doi:10.18576/ncmsel/010104.
Ali, K. K., Shaalan, M. A. and Raslan, K. R. (2019), ‘An extended theoretical and numerical study of two-point boundary value problems using collocation method with physical applications’, Numerical and Computational Methods in Sciences and Engineering, 1(1), pp. 33–39. Available at: https://doi.org/10.18576/ncmsel/010104.
Ali, Khalid K., et al. “An Extended Theoretical and Numerical Study of Two-point Boundary Value Problems Using Collocation Method with Physical Applications.” Numerical and Computational Methods in Sciences and Engineering, vol. 1, no. 1, 2019, pp. 33–39. https://doi.org/10.18576/ncmsel/010104.
Ali, Khalid K., M. A. Shaalan, and K. R. Raslan. “An Extended Theoretical and Numerical Study of Two-point Boundary Value Problems Using Collocation Method with Physical Applications.” Numerical and Computational Methods in Sciences and Engineering 1, no. 1 (2019): 33–39. https://doi.org/10.18576/ncmsel/010104.
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Published by: Engineering Journals
