[1] Ä°. DaÄŸ, D. Irk and B. Saka, A numerical solution of the
Burgers’ equation using cubic B-splines, Applied Mathematics
and Computation 163(1) (2005), 199-211.
DOI: https://doi.org/10.1016/j.amc.2004.01.028
[2] Ä°. DaÄŸ, B. Saka and A. Boz, B-spline Galerkin methods for
numerical solutions of the Burgers’ equation, Applied
Mathematics and Computation 166(3) (2005), 506-522.
DOI: https://doi.org/10.1016/j.amc.2004.06.078
[3] I. Dag, B. Saka and A. Boz, B-spline Galerkin methods for
numerical solutions of the Burgers equation, Applied Mathematics and
Computation 166(3) (2005), 506-522.
DOI: https://doi.org/10.1016/j.amc.2004.06.078
[4] O. Ersoy, I. Dag and N. Adar, The Exponential Cubic B-spline
Algorithm for Burgers’s Equation, arXiv: Numerical Analysis
(2016).
[5] C. A. J. Fletcher, Generating exact solutions of the
two-dimensional Burgers’ equation, International Journal for
Numerical Methods in Fluids 3(3) (1983), 213-216.
DOI: https://doi.org/10.1002/fld.1650030302
[6] T. Geyikli and S. B. Gazi Karakoc, Septic B-spline collocation
method for the numerical solution of the modified equal width wave
equation, Applied Mathematics 2(6) (2011), 739-749.
DOI: https://doi.org/10.4236/am.2011.26098
[7] K. Kakuda and N. Tosaka, The generalized boundary element approach
to Burgers’ equation, International Journal for Numerical
Methods in Engineering 29(2) (1990), 245-261.
DOI: https://doi.org/10.1002/nme.1620290203
[8] P. K. Srivastava, Study of differential equations with their
polynomial and non-polynomial spline based approximation, Acta Tehnica
Corviniensis: Bulletin of Engineering 7(3) (2014), 139-150.
[9] S. Kutluay, A. Esen and I. Dag, Numerical solutions of the
Burgers’ equation by the least-squares quadratic B-spline
finite element method, Journal of Computational and Applied
Mathematics 167(1) (2004), 21-33.
DOI: https://doi.org/10.1016/j.cam.2003.09.043
[10] W. G. Bickley, Piecewise cubic interpolation and two-point
boundary problems, Computer Journal 11(2) (1968), 206-208.
DOI: https://doi.org/10.1093/comjnl/11.2.206
[11] W. Liu, A asymptotic behavior of solutions of time-delayed
Burgers’ equation, Discrete and Continuous Dynamical Systems,
Series B, 2(1) (2002), 47-56.
DOI: https://doi.org/10.3934/dcdsb.2002.2.47
[12] H. Nguyen and J. Reynen, A space time finite element approach to
Burgers’ equation, E. Hinton et al. (editors), Numerical
Methods for Non-Linear Problems, Volume 3, Pineridge Press, pp.
718-728 (1987).
[13] K. Parcha and N. L. Mihretu, Solutions of seventh order boundary
value problems using ninth degree spline functions and comparison with
eighth degree spline solutions, Journal of Applied Mathematics and
Physics 4(2) (2016), 249-261.
DOI: https://doi.org/10.4236/jamp.2016.42032
[14] P. M. Printer, Splines and Variational Methods, Colorado State
University, Wiley Classics Edition Published 57 (1975), 421-421.
[15] M. A. Ramadan, T. S. El-Danaf and F. E. I. Abd Alaal, A numerical
solution of the Burgers’ equation using septic B-splines,
Chaos, Solitons and Fractals 26(4) (2005), 1249-1258.
DOI: https://doi.org/10.1016/j.chaos.2005.02.019
[16] J. Rashidinia, M. Khazaei and H. Nikmarvani, Spline collocation
method for solution of higher order linear boundary value problems,
TWMS Journal of Pure and Applied Mathematics 6(1) (2015), 38-47.
[17] H. Bateman, Some recent researches on the motion of fluids,
Monthly Weather Review 43(4) (1915), 163-170.
DOI: https://doi.org/10.1175/1520-0493(1915)43<163:SRROTM>2.0.CO;2
[18] J. M. Burger, A mathematical model illustrating the theory of
turbulence, Advanced in Applied Mechanic 1 (1948), 171-199.
DOI: https://doi.org/10.1016/S0065-2156(08)70100-5
[19] J. Rashidinia and Sh. Sharifi, Survey of B-spline functions to
approximate the solution of mathematical problems, Mathematical
Sciences 6 (2012); Article 48.
DOI: https://doi.org/10.1186/2251-7456-6-48
[20] K. R. Raslan, A collocation solution for Burgers equation using
quadratic B-spline finite elements, International Journal of Computer
Mathematics 80(7) (2003), 931-938.
DOI: https://doi.org/10.1080/0020716031000079554
[21] B. Saka, Ä°. DaÄŸ and A. Boz, Quintic B-Spline Galerkin
Method for Numerical Solutions of the Burgers’ Equation
(2004).
[22] T. E. Sayed and A. E. Danaf, Numerical solution of the
Korteweg–Vries Burgers equation by quintic spline method,
Studia Universitatis Babes-Bolyai Mathematica 47 (2002), 41-55.
[23] M. Shearer and R. Levy, Partial Differential Equations:
Introduction to Theory and Applications, Princeton University Press
(2015), 175-176.
[24] H. S. Shukla, M. Tamsir, V. K. Srivastava and J. Kumar, Numerical
solution of two dimensional coupled viscous Burger equation using
modified cubic B-spline differential quadrature method, AIP Advanced
4(11) (2015); Article 117134.
DOI: https://doi.org/10.1063/1.4902507
[25] P. K. Srivastava, Application of higher order splines for
boundary value problems, International Journal of Mathematical and
Computational Sciences 9(2) (2015), 115-122.
DOI: https://doi.org/10.5281/zenodo.1107165
[26] E. VaroÄŸlu and W. D. L. Finn, Space-time finite elements
incorporating characteristics for the Burgers’ equation,
International Journal for Numerical Methods in Engineering 16(1)
(1980), 171-184.
DOI: https://doi.org/10.1002/nme.1620160112
[27] M. Khazaei and Y. Karamipour, Numerical Solution of The Seventh
Order Boundary Value Problems using B-spline Method,
arXiv:2109.06030v1 [math.NA], arXiv:2109.06030 [math.NA].
[28] M. A. Khater, Y. M Chu, R. A. M. Attia, M. Inc and D. Lu, On the
analytical and numerical solutions in the quantum magnetoplasmas: The
atangana conformable derivative (1+3)-ZK equation with power-law
nonlinearity, Hindawi, Advances in Mathematical Physics (2020);
Article ID 5809289.
DOI: https://doi.org/10.1155/2020/5809289
[29] S. Akter, M. G. Hafez, Yu-Ming Chu and M. D. Hossain, Analytic
wave solutions of beta space fractional Burgers equation to study the
interactions of multi-shocks in thin viscoelastic tube filled,
Alexandria Engineering Journal 60(1) (2021), 877-887.
DOI: https://doi.org/10.1016/j.aej.2020.10.016
[30] H. Ramos, A. Kaur and V. Kanwar, Using a cubic B-spline method in
conjunction with a one-step optimized hybrid block approach to solve
nonlinear partial differential equations, Computational and Applied
Mathematics 41(1) (2022); Article 34.
DOI: https://doi.org/10.1007/s40314-021-01729-7