츨…<L. t-o(see (1) in Section i2 4) s bject to the given conditions. Solve the wave equation, .a a r u(0, t)=0, u(T, t)=0, t> 0 ux, o) 0.01 sin(5tx), 0u t=0 u(x, t) = n=1 Need Help? LRead it ....
Solve the initial-boundary value problem for the following equation
U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0
Q4| (5 Marks)
my question
please answer
Solve the initial-boundary value problem for the
following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0,
and U, (N, t) = 0 Q4| (5 Marks)
Solve the initial-boundary value problem for the following equation Uų...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
Solve the wave equation
a2
∂2u
∂x2
=
∂2u
∂t2
, 0 < x < L, t > 0
(see (1) in Section 12.4) subject to the given conditions.
u(0, t) = 0, u(L, t) = 0
u(x, 0) =
4hx
L
,
0
<
x
<
L
2
4h
1 −
x
L
,
L
2
≤
x
<
L
,
∂u
∂t
t = 0
= 0
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3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0 < x< 1 with boundary conditions ux(0, t) = 0 and ux(1, t) yields the general solution, 1, 0<x < 1/2 0, 1/2 x<1 Determine the coefficients An (n = 0, 1, 2, . . .) when u(x,0) = f(x) =
3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
(1 point) Solve the wave equation with fixed endpoints and the given initial displacement and velocity. a2 ,0<x<L, t > 0 a(0. t) = 0, u(L, t) = 0, t > 0 Ou Ot ηπα t) + B,, sin (m Now we can solve the PDE using the series solution u(r,t)-> An C computed many times: An example: t) ) sin (-1 ). The coefficients .An and i, are Fourier coefficients we have , cos n-1 sin(n pix/ L) dr...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (π ,t )-0 and V (x,0) sin 3x
Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (π ,t )-0 and V (x,0) sin 3x