(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

Expert Solution

Colby Messinger answered 2 years ago

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.

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

Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...

Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x < 1, 0 < t < 1 BCs: ⇢ u(0, t) = 0 ux(1, t) = 0 0 < t < 1 IC: u(x, 0) = sin(pi x) 0 x  1 for t = 0.005, 0.010, 0.015 by the explicit method. Assume

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

(PDE) Write the soln using separation of variables , in the form of fourir series: Utt=Uxx...

(PDE) Write the soln using separation of variables , in the form of fourir series: Utt=Uxx boundary: U(t,0)=0=U(t,pi) initial : initial: U(0,x)=1 and Ut(0,x)=0

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x, 0) = π/2 − |x − π/2|

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

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, u(0,t) = 0 = u(1,t), u(x,0) = x/2

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

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1, t > 0, ux(0,t) = 0 = ux(1,t), u(x,0) = 1 - x2

Question

(PDE) Find the series soln to Ut=Uxx on -2<x<2, T>0 with Dirichlet boundary { U(t,-2)=0=U(t, 2)...

Solutions

Expert Solution

Related Solutions

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

Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...

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

(PDE) Write the soln using separation of variables , in the form of fourir series: Utt=Uxx...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

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

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...

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 < 1,...