Name: Anonymous 2007-10-10 22:37
u_tt - 4 u_xx = 0
initial conditions: u(x,0) = 0, u_t(x,0) = 0
in R = {(x,t) | 0<=x<=1, t>=0}
boundary conditions: u(0,t) = 0, u_x(1,t) = f(t)
in t>=0
v(x,t) = u_t + 2 u_x
w(x,t) = u_t - 2 u_x
I know you are supposed to approximate u(x,t) but you can find v and w. What I really can't figure out is how to find u_t(1,t) and u_x(0,t).
I know you use d'Alembert formula to find u(x,t) with just the initial conditions but I have no idea how to do this with the boundary conditions. Can you refer me to how to do this with boundary condition and also, how do I finded out v(1,t) and w(0,t)?
initial conditions: u(x,0) = 0, u_t(x,0) = 0
in R = {(x,t) | 0<=x<=1, t>=0}
boundary conditions: u(0,t) = 0, u_x(1,t) = f(t)
in t>=0
v(x,t) = u_t + 2 u_x
w(x,t) = u_t - 2 u_x
I know you are supposed to approximate u(x,t) but you can find v and w. What I really can't figure out is how to find u_t(1,t) and u_x(0,t).
I know you use d'Alembert formula to find u(x,t) with just the initial conditions but I have no idea how to do this with the boundary conditions. Can you refer me to how to do this with boundary condition and also, how do I finded out v(1,t) and w(0,t)?