Re: 2+ D wave equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg54369] Re: 2+ D wave equation*From*: highegg at centrum.cz (highegg)*Date*: Sat, 19 Feb 2005 02:32:26 -0500 (EST)*References*: <7bo0ra$dpk@smc.vnet.net>, <5zpielxbszwk@legacy>*Sender*: owner-wri-mathgroup at wolfram.com

On 17 Feb 05 23:46:19 -0500 (EST), mohammad kazim wrote: >I'm facing the same problem someone else posted (pasted below)about 6 >years ago. Unfortunately, nobody responded back then. > >I'm trying to numerically obtain the answer for a vibrating >rectangular membrane. Therefore, I need to describe a 2 spatial >dimensional wave equation, and I'm trying to use NDSolve. > >Thanks! > >On 5 Mar 1999 02:24:26 -0500, Robert Walgate wrote: >>MathGroup >> >> A question: I need to find numerical solutions of the wave equation >in 2 >>or more spatial dimensions, with various boundary conditions. NDSolve >>limits the problem to one spatial dimension. Has anyone created a >package >>to go to higher dimensions? >> >>(Dr) Robert Walgate >>Open Solutions NDSolve isn't limited to 1D equations, at least in version 5.1. For example, this solves a 2D wave equation: First[NDSolve[{ D[u[x, y, t], {t, 2}] == D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}], u[x, y, 0] == 0, Derivative[0, 0, 1][u][x, y, 0] == -0.5*x(1 - x)*y(1 - y), u[0, y, t] == 0, u[1, y, t] == 0, u[x, 0, t] == 0, u[x, 1, t] == 0}, u, {x, 0, 1}, {y, 0, 1}, {t, 0, 10}]] NDSolve is though limited to finite differences (on rect. regions), but the implementation of FD is very sophisticated. Regards Jaroslav Hajek