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Solve the following problems: ut(x, t)--uxx (x, t) n(x,t), i, (x, t ) → 0, u(x,0) - e-' u, (x,t) ...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), usi...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
1 point) Solve the nonhomogeneous heat problem ut=uxx+4sin(2x), 0<x<π,ut=uxx+4sin(2x), 0<x<π, u(0,t)=0, u(π,t)=0u(0,t)=0, u(π,t)=0 u(x,0)=5sin(5x)u(x,0)=5sin(5x) u(x,t)=u(x,t)= Ste
1 point) Solve the nonhomogeneous heat problem
ut=uxx+4sin(2x), 0<x<π,ut=uxx+4sin(2x), 0<x<π,
u(0,t)=0, u(π,t)=0u(0,t)=0, u(π,t)=0
u(x,0)=5sin(5x)u(x,0)=5sin(5x)
u(x,t)=u(x,t)=
Steady State Solution limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the nonhomogeneous heat problem Ut = Uxx + 4 sin(2x), 0< x < , u(0,1) = 0, tu(T, t) = 0 u(x,0) = 5 sin(52) u(a,t) Steady State Solution limt u(x, t) = Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts...
Solve the heat problem ut=uxx−cos(x), 0<x<π, ut=uxx−cos(x), 0<x&l...
Solve the heat problem ut=uxx−cos(x), 0<x<π, ut=uxx−cos(x), 0<x<π, ux(0,t)=0, ux(π,t)=0 ux(0,t)=0, ux(π,t)=0 u(x,0)=1u(x,0)=1 u(x,t)= ?
(1) (4 points) Let L 〉 0 be a given constant. Solve ut = uxx u(0,t)...
(1) (4 points) Let L 〉 0 be a given constant. Solve ut = uxx u(0,t) = u(L, t) = 0 u(x, 0) = sin2 (2x) for all (x, tje (0,L) × (0,+oo), for all t > 0, for all x e [0, L]
Solve the Dirichlet problem in an infinite strip uxx + uyy=0 for x ϵ R and 0 <y <b , u(x,0)=f(x) , u(x,b)=g(x). (...
Solve the Dirichlet problem in an infinite strip
uxx + uyy=0
for x ϵ R and 0 <y <b ,
u(x,0)=f(x) ,
u(x,b)=g(x). (Hint: first
do the case f=0. The case g=0 reduces to this one
by the substitution y→ b-y , and the case general is
obtained by superposition)
4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g...
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) +...
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =
(1 point) Solve the nonhomogeneous heat problem ut = Uxx + sin(3x), 0 < x <...
(1 point) Solve the nonhomogeneous heat problem ut = Uxx + sin(3x), 0 < x < 1, u(0,t) = 0, u1,t) = 0 u(x,0) = 2 sin(4x) u(x, t) = Steady State Solution limt-001(x, t) = ((sin(3x))/9)
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
Problem # 3 [20 Points] Solve PDE: ut = uxx - u, 0 < x < 1, 0 < t < ∞ BCs: u(0, t)=0 u(1, t)=0 0 < t < ∞ IC: u(x, 0) = sin(πx), 0 ≤ x ≤ 1 directly by separation of variabl...
Problem # 3 [20 Points] Solve PDE: ut = uxx - u, 0 < x < 1, 0 < t < ∞ BCs: u(0, t)=0 u(1, t)=0 0 < t < ∞ IC: u(x, 0) = sin(πx), 0 ≤ x ≤ 1 directly by separation of variables without making any preliminary trans- formation. Does your solution agree with the solution you would obtain if transformation u(x, t)= e(caret)(-t) w(x, t) were made in advance?
Use fourier transform to solve the following BVP
Use Fourier transform to solve the following BVP Utt-Uxx=F(x,t) 0<x<1,t>0u(x,0)=f(x)ut(x,0)=0u(0,t)=ux(1,t)=0
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
1 point) Solve the nonhomogeneous heat problem
ut=uxx+4sin(2x), 0<x<π,ut=uxx+4sin(2x), 0<x<π,
u(0,t)=0, u(π,t)=0u(0,t)=0, u(π,t)=0
u(x,0)=5sin(5x)u(x,0)=5sin(5x)
u(x,t)=u(x,t)=
Steady State Solution limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the nonhomogeneous heat problem Ut = Uxx + 4 sin(2x), 0< x < , u(0,1) = 0, tu(T, t) = 0 u(x,0) = 5 sin(52) u(a,t) Steady State Solution limt u(x, t) = Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts...
(1) (4 points) Let L 〉 0 be a given constant. Solve ut = uxx u(0,t) = u(L, t) = 0 u(x, 0) = sin2 (2x) for all (x, tje (0,L) × (0,+oo), for all t > 0, for all x e [0, L]
Solve the Dirichlet problem in an infinite strip
uxx + uyy=0
for x ϵ R and 0 <y <b ,
u(x,0)=f(x) ,
u(x,b)=g(x). (Hint: first
do the case f=0. The case g=0 reduces to this one
by the substitution y→ b-y , and the case general is
obtained by superposition)
4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g...
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =
(1 point) Solve the nonhomogeneous heat problem ut = Uxx + sin(3x), 0 < x < 1, u(0,t) = 0, u1,t) = 0 u(x,0) = 2 sin(4x) u(x, t) = Steady State Solution limt-001(x, t) = ((sin(3x))/9)
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
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