Question

In: Advanced Math

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

Consider the equation utt = uxx

x ∈ (0, pi)

ux(0,t) = u(pi,t) = 0

Write the series expansion for a solution u(x,t)

Solutions

Expert Solution


Related Solutions

Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi
Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi
Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1
Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1
Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0
Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi,...
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx, ut(x,0) = pi - x
Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...
Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx - sin3x
For the wave equation, utt = c2uxx, with the following boundary and initial conditions, u(x, 0)...
For the wave equation, utt = c2uxx, with the following boundary and initial conditions, u(x, 0) = 0 ut(x, 0) = 0.1x(π − x) u(0,t) = u(π,t) = 0 (a) Solve the problem using the separation of variables. (b) Solve the problem using D’Alembert’s solution. Hint: I would suggest doing an odd expansion of ut(x,0) first; the final solution should be exactly like the one in (a).
Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x), u(0,x)= 0 , Ut(0,x)...
Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x), u(0,x)= 0 , Ut(0,x) = 0. Is h(t) = u(t,0) a periodic function? (PDE)
Consider the equation: ?̇ +2? = ?(?) with initial condition x(0) = 2 (a) If u(t)...
Consider the equation: ?̇ +2? = ?(?) with initial condition x(0) = 2 (a) If u(t) = 0, find the solution ?(?). What is ?(?) as t -> ∞? (b) If u(t) = 4+t, find the solution ?(?). What is ?(?) as t -> ∞? (c) If u(t) = ?3?, find the solution ?(?). What is ?(?) as t -> ∞? (d) If u(t) = δ(t), find the solution ?(?). What is ?(?) as t -> ∞?
(PDE) Find the series soln to Ut=Uxx on -2<x<2, T>0 with Dirichlet boundary { U(t,-2)=0=U(t, 2)...
(PDE) Find the series soln to Ut=Uxx on -2<x<2, T>0 with Dirichlet boundary { U(t,-2)=0=U(t, 2) initial condition { U(0,x) = { x, IxI <1
Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0,...
Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0, y) = 0, u(1, y) = 0.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT