5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r) 5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r)
5. Solve Au=0, r>1, 0 < θ < 2π, u(1.0) = cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
Please solve as if you didnt have the answer. 5. Solve u(a,0) = 0 ( 2) Answer: u ( r, θ) =-( a2-r
5. Solve Au=0, r>1, 0 < θ < 2π, a(1,0) cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
30] Find th e solution of the following boundary value problem. 1<r<2, u(r, θ = 0) = 0, u(r, θ = π) =0, 1,0-0, u(r-2,0)-sin(20), 0 < θ < π. u(r Please also draw the sketch associated with this problem. You may assume that An -n2, Hn(s)sin(ns), n 1,2,3,. are the eigenpairs for the eigenvalue problem H(0) 0, H(T)0. 30] Find th e solution of the following boundary value problem. 1
42.(a) Solve for u(r, θ): u,( 1,0)-0, u(23)-40. That is, the region is an annulus betweenr 1 and r-2 HINT: First draw a picture of it, to get a look at the problem. Now, you should be able to readily get u(r, θ)-(A+B In r) (C+D6) + (Er"+FF") (Geosx8+ Hsinx8). Then, see that you have 2n-periodicity, so K n (n-1,2,..) and D-0, so u ( r, θ)-A" + B. In r + an infinite series with r's and θ's in...
Solve the circularly symmetric vibrating membrane PDE given as u_tt = ∇^2*u BC : u(1, θ, 0) = 0, 0 < t < ∞ ICs : u(r, θ, 0) = J_0*(2.4r) − 0.25*J_0*(14.93r), 0 ≤ r ≤ 1 u_t(r, θ, 0) = 0 Solve the circularly symmetric vibrating membrane PDE given as Utt = Dau BC : u(1,0,0) = 0, 0<t< oo ICs : u(r,0,0) = J.(2.4r) – 0.25J(14.93r), 0 <r <1 Ut(r,0,0) = 0
All of them please if you can 6. Solve the Dirichlet problem 0<r<3 la(3.0) = 1-cos0+ 2 sin 20. θ < 2π 0 7. Solve the Dirichlet problem lu(3,0) = 3-2 sin θ + cos 20, θ 0 2π 8. Solve the Dirichlet problem a(3,0) 2 + sin 20, 0 θ<2π 6. Solve the Dirichlet problem 0
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1. 9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1.
3. (a) Solve the boundary value problem on the wedge u(r, 0) = 0 0<r<p, a(r, g) = 0 0<r<p, u(p, 0)-/(0), 0 < θ < θο. (b) State the mathematical and physical boundary conditions for this problem. (c) Suppose ρ-1.00-π/3, and f(9)-66ere. Plot the solution surface and polar contour plot for N -10 3. (a) Solve the boundary value problem on the wedge u(r, 0) = 0 0