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Wang, Chi-Chang; Liao, Wu-Jung; Hsu, Yin-Sung

Hybrid spline difference method for the Burgers’ equation. (English) Zbl 1288.65127

Appl. Math. Comput. 219, No. 3, 1031-1039 (2012).
Summary: This study develops a high accuracy hybrid spline difference method, and deduces a difference equation that is very similar to finite difference method from the concept of spline difference. As validated by nonlinear Burgers’ equation, the concept of difference makes the computational process as simple as the finite difference method, and easy to be implemented. The free parameters \(\alpha\to 1/12\) and \(\alpha\to 1/6\) are combined in the concept of spline hybrid, in order to increase the accuracy of the first and second derivatives of space from \(O(h^{2})\) of finite difference method to the \(O(h^{4})\). The accuracy is improved, and the numerical oscillation with the increase in parameter \(R_{e}\) is improved greatly.

Cited in 2 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

hybrid spline difference method; Burgers’ equation; parametric spline; finite difference method; high accuracy; numerical examples
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References:

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