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)
