2. Use eigenfunction expansion to solve the following IBVP:
please answer v) (fifth one)
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2. Use eigenfunction expansion to solve the following IBVP: please answer v) (fifth one) 2. Use...
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
Solve the following IBVP by eigenfunction expansion.$$ u_{t t}=u_{x x}+1+t \cos (\pi x), \quad 0<x<1, quad="" t="">0 $$$$ u_{x}(0, t)=0 \quad \text { and } \quad u_{x}(1, t)=0, \quad t>0 $$$$ u(x, 0)=2 \quad \text { and } \quad u_{t}(x, 0)=-2 \cos (2 \pi x), \quad 0<x<1 $$
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t) + 2t sin (2na:) , 0 < x < 1, 0, u(1,t)=0, t > 0, sin(2π.r)-5 sin (4π.r) , 0 < x < 1. t > 0, = = = 4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t)...
2. Use separation of variables to solve the IBVP: utt (z, y, t) u(0, y, t) u (x, y,0) uzz(z, y, t) + un, (x, y, t) = 0, 0 < x < 1, 0 < y < 1, 0, u(1,y,t)=0, u(z,0,t)=0, u(z, l,t) = 0 sin(r) sin (2my), ue (r, y,02 sin(2mx) sin(ry) t > 0, = =
(3 points) Use eigenvalues and eigenfunction expansion expansion to solve the Dirichlet problem Δυ(x,y)-0 on the rectangle {(x, y):0
3. Use separation of variables to compute the first five terms of the series solution of the IBVP: urr (r,0) + r-rur (r, θ u (1,0, t) 0, u (r, θ, t) , ur(r, θ, t) bounded as r-+0+,-π < θ < π, t > 0, u (r,0,0) = r sin θ, ut (r.0, 0) = 0, o < r < 1, -π < θ < π. Hint: Follow the example from Lecture 19 and use the fact that with...
This is a partial differential equations question. Please help me solve for u(x,t): Find the eigenvalues/eigenfunction and then use the initial conditions/boundary conditions to find Fourier coefficients for the equation. 3. (10 pts) Use the method of separating variables to solve the problem utt = curr u(0,t) = 0 = u(l,t) ur. 0) = 3.7 - 4, u(3,0) = 0 for 0 <r<l, t>0 fort > 0 for 0 <r<1
Please show all work and answer all parts of the question. Please do not repost the question and if you do please at least include the actual code and not the written answer that is incorrect to other posts. Consider the initial boundary value problem (IBVP) for the 1-D wave equation on a finite domain: y(0,t) 0, t > 0 t > 0 y(1,0) f(x) where f(x) =-sin ( 2 π-π (a) Plot the initial condition f(x) on the given...
(1 point) Use eigenvalues and elgenfunction expansion expansion to solve the mixed Dirichlet- Neumann problem for the Laplace equation Au(x, y) = 0 on the rectangle {(x,y) : 0<x<1, 0<y<1} satisfying the BCS ux(0,y) = 0, ux(1, y) = 0, 0 < y < 1 u(x,0) = x, u(x, 1) = 0, 0<x<1 The solution can be written as The u(x, y) = Covo(y)+(x) + .(x).(y) where on is a normalized eigenfunction for "(x) = 10(x) with x(0) = 0...
1) (15 marks) Consider the following PDHE Uz(0, t) = 0, u(5,t)=1, t>0 u(x, 0)- 20 exp(-2), 0<x<!5 (a) Solve using separation of variables. You may leave the eigenfunction expansion coef (b) Plot the solution at t-1,3,5 and 30, along with the initial condition and steady state ficients in inner product form. solution, using 15 terms in your truncated expansion. You may use mupad to evaluate the eigenfunction expansion coefficients from part (a) which you left in inner product form...