Wave Equation

Description

Two dimensitonal wave propogation on a mesh cloth with a length of L and a width of W described by the wave equation u(x, y, t) with utt(x, y, t) = c2 (uxx(x, y, t) + uyy(x, y, t)) where c = 1 is drawn as t increases. Two cases are considered depending on whether the simulation starts (i) without any impulse or (ii) impulsively. In the first case, the initial conditions are u(x, y, 0) = I(x, y) where I(x, y) is the PDF of bivariate normal distribution and ut(x, y, 0) = 0. In the second case, the conditions are u(x, y, 0) = 0 and ut(x, y, 0) = V(x, y) where V(x, y) represents a boxlike impulse. Fixed boundary conditions are considered: u(0, 0, t) = u(L, 0, t) = u(W, 0, t) = u(W, L, t) = 0. A numerical analysis is employed. For this, differential equations are discrtetized into difference equations using centered, finite difference methods.

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