On a seventh order convergent weakly L-stable Newton Cotes formula with application on Burger's equation
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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.
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