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Zhu, Chun-Gang; Wang, Ren-Hong

Numerical solution of Burgers’ equation by cubic B-spline quasi-interpolation. (English) Zbl 1159.65087

Appl. Math. Comput. 208, No. 1, 260-272 (2009).
Summary: A numerical solution of the Burgers’ equation is presented based on cubic B-spline quasi-interpolation. At first the cubic B-spline quasi-interpolation is introduced. Moreover, a numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. The accuracy of the proposed method is demonstrated by some test problems. The numerical results are found in good agreement with the exact solutions. The advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.

Cited in 1 Review
Cited in 35 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

Burgers’ equation; B-spline; quasi-interpolation; second-order hyperbolic equation; numerical examples; numerical results; algorithm
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\textit{C.-G. Zhu} and \textit{R.-H. Wang}, Appl. Math. Comput. 208, No. 1, 260--272 (2009; Zbl 1159.65087)
Full Text: DOI

References:

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