Burgers’ equation with high Reynolds number

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Abstract
Burgers’ equation, involving very high Reynolds numbers, is numerically solved by using a new approach based on the distributed approximating functional for representing spatial derivatives of the velocity field. For moderately large Reynolds numbers, this simple approach can provide very high accuracy while using a small number of grid points. In the case where the Reynolds number ⩾105, the exact solution is not available and a discrepancy exists in the literature. Our results clarify the behavior of the solution under these conditions.