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: U_tt-a²u_xx=0, 0≤x≤1, 0≤t<∞

BCs: u(0,t)=0

u(1,t)=cos(t)

u(x,0)=0

u_t(x,0)=0

Expert Solution

Colby Messinger answered 1 year ago

Solve the initial value problem Utt = c^2Uxx, u(0,x)= e^-x^2 , Ut(0,x) = sin x (PDE)

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)

(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

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

Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0,...

Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0, U(0,t) = U(π,t) = 0, t > 0, U(x, 0) = e^(π), 0 ≤ x ≤ π.

u'' + sinu = sinx (-1<x<1) u(-1)=1, u'(1)=0 solve this boundary value problem.

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R. c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight line x = t, where f is a given function.

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 following initial value problem ut + 2ux − 2u = e t+2x , u(x,...

Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x, 0) = 0

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).

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