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Open AccessArticle

A High-Order Weakly L-Stable Time Integration Scheme with an Application to Burgers’ Equation

1
Department of Mathematics, Indian Institute of Technology Patna, Patna, Bihar 801106, India
2
Department of Mathematics, Texas A&M, University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA
*
Author to whom correspondence should be addressed.
Computation 2020, 8(3), 72; https://doi.org/10.3390/computation8030072
Received: 13 July 2020 / Revised: 3 August 2020 / Accepted: 4 August 2020 / Published: 9 August 2020
(This article belongs to the Section Computational Engineering)
In this paper, we propose a 7th order weakly L-stable time integration scheme. In the process of derivation of the scheme, we use explicit backward Taylor’s polynomial approximation of sixth-order and Hermite interpolation polynomial approximation of fifth order. We apply this formula in the vector form in order to solve Burger’s equation, which is a simplified form of Navier-Stokes equation. The literature survey reveals that several methods fail to capture the solutions in the presence of inconsistency and for small values of viscosity, e.g., 103, whereas the present scheme produces highly accurate results. To check the effectiveness of the scheme, we examine it over six test problems and generate several tables and figures. All of the calculations are executed with the help of Mathematica 11.3. The stability and convergence of the scheme are also discussed. View Full-Text
Keywords: Hermite interpolation; L-stable; A-stable; weakly L-stable; Burgers’ equation Hermite interpolation; L-stable; A-stable; weakly L-stable; Burgers’ equation
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Verma, A.K.; Rawani, M.K.; Agarwal, R.P. A High-Order Weakly L-Stable Time Integration Scheme with an Application to Burgers’ Equation. Computation 2020, 8, 72.

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