19-22 October 2011
Hotel Roanoke, Roanoke VA
US/Eastern timezone
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An Averaged-Separation of Variable Solution to the Burger Equation

22 Oct 2011, 11:45
12m
Crystal Ballroom B (Hotel Roanoke, Roanoke VA)

Crystal Ballroom B

Hotel Roanoke, Roanoke VA

Speaker

Dr 'Kale Oyedeji (Morehouse College)

Description

The Burger Partial Differential Equation (PDE) provides a nonlinear model that incorporates several of the important properties of fluid behavior. However, no general solution to it is known for given arbitrary initial and/or boundary conditions. We propose a "new" method for determining approximations for the solutions. Our method combines the separation of variables technique, combined with an averaging over the space variable. A test of this procedure is made for the following problem, where u = u(x,t): 0 <= x <= 1, t > 0, u(0,t) = 0, u(1,t) = 0, u(x,0) = x(1-x), u_t + u u_x = D u_{xx}, where D is a non-negative parameter. The validity of the calculated solution is made by comparing it to an exact analytic solution, as well as an accurate numerical solution for the special case where D = 0.

Co-author

Ronald Mickens (Clark Atlanta University)

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