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Firstly , we find eigen function by boundary conditions...
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u...
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
2. Use eigenfunction expansion to solve the following IBVP: please answer v) (fifth one) 2. Use eigenfunction expansion to solve the following IBVP u,(x.t)-u(x.t)+(t-1)sin(a) 0<x<1 t>0 u(0,t)0, u(l,r) 0, t>0 u,(x,t)(x) cos(z), 0 <x<1 t>0 n(x,0) = 2-cos(32t) 0 < x < 1 u(0,0, u(l,t) 0, t>0 n(x,0) = 1 u,(x,0) = 0 0 < x < 1 IV Hm(x,y)+u" (x,y)--r', 0<x<1 0<y<2 u(x,0) = 0, u(x2) =-x 0 < x < 1 v) 7" 11(0,8) bounded , -π<θ<π
nonhomogeneous vibrating string problem for u(x with homogeneous boundary conditions t > 0 u(0, t) u(r,t) = 0, 0, = and the initial conditions 0stst tr(z,0)=0, u(z, 0) sin(2x), = Find the solution u(x,t) to the IBVP using an eigenfunction expansion: u(z, t) = Σ an(t) sin(nz) n-1 nonhomogeneous vibrating string problem for u(x with homogeneous boundary conditions t > 0 u(0, t) u(r,t) = 0, 0, = and the initial conditions 0stst tr(z,0)=0, u(z, 0) sin(2x), = Find the...
Solve the following IBVP by eigenfunction expansion.$$ u_{t t}=u_{x x}+1+t \cos (\pi x), \quad 0<x<1, quad="" t="">0 $$$$ u_{x}(0, t)=0 \quad \text { and } \quad u_{x}(1, t)=0, \quad t>0 $$$$ u(x, 0)=2 \quad \text { and } \quad u_{t}(x, 0)=-2 \cos (2 \pi x), \quad 0<x<1 $$
Which of the following functions is the unique solution of the IBVP Ut = QUI 0<< t > 0 u(0,t) = u(Tt, t) = 0, t> 0 u(2,0) = 1, 0 <<< Select one: 2((-1)" – 1) O A. u(x, t) = -sin(nt)e-amt nyt T21 00 2(1 - (-1)") O B. u(x,t) = -sin(na)e-an’t nn 11 2(1 – (-1)") O C. u(a,t) -sin(ne)eamt n n=1 00 2((-1)" – 1) O D. u(2,t) = sin(nx)e-ant n 11 20 (1-(-1)") O E....
Problem 1. Consider the nonhomogeneous heat equation for u,t) ut = uzz + sin(2x), 0<x<π, t>0 subject to the nonhomogeneous boundary conditions u(0, t) t > 0 u(n, t) = 0, 1, - and the initial condition Lee) Find the solution u(z, t) by completing each of the following steps: (a) Find the equilibrium temperature distribution ue(x). (b) Denote v(x, t) u(a, t) - e(). Derive the IBVP for the function v(x,t). (c) Find v(x, t) (d) Find u(, t)...
Find solution to the IBVP PDE BCs Ic u(0, t)-0, 0<oo l u(1, t) 0, 0<t< oo u(z,0)=x-x2ババ1
4. (XX pts.) Find solution to the IBVP PDE BCs IC a(0, t) = 0, a(1,t)=0. () < t < oo () < t
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...
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...