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On a seventh order convergent weakly $L$-stable Newton Cotes formula with application on Burger's equation | | Amit Kumar Verma
; Mukesh Kumar Rawani
; Ravi P. Agarwal
; | | Date: |
12 Nov 2019 | | Abstract: | In this paper we derive $7^{th}$ order convergent integration formula in time
which is weakly $L$-stable. To derive the method we use, Newton Cotes formula,
fifth-order Hermite interpolation polynomial approximation (osculatory
interpolation) and sixth-order explicit backward Taylor’s polynomial
approximation. The vector form of this formula is used to solve Burger’s
equation which is one dimensional form of Navier-Stokes equation. We observe
that the method gives high accuracy results in the case of inconsistencies as
well as for small values of viscosity, e.g., $10^{-3}$. Computations are
performed by using Mathematica 11.3. Stability and convergence of the schemes
are also proved. To check the efficiency of the method we considered 6 test
examples and several tables and figures are generated which verify all results
of the paper. | | Source: | arXiv, 1911.5556 | | Services: | Forum | Review | PDF | Favorites | |
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