(4 points) This problem is concerned with solving an initial boundary value problem for the heat ...
(1 point) This problem is concerned with solving an initial boundary value problem for the heat equation: (0,t)-0, t0 u,o)- in the form, ie where the term involving cy may be missing. Here y is the eigenfunction for Ay- 0 so if zero is not an eigenvalue then this term will be zero First find the eigenvalues and orthonormal eigenfunctions for n1.iA. Pa(x). For n 0 there may or may not be an eigenpair. Give all these as a comma...
x < n with BCs y(0)= 0 and y(z) 0. (1 point) Find the eigenvalues and eigenfunctions for y" = Ay on 0 Note that any constant times an eigenfunction is also an eigenfunction. In order to obtain a unique solution find (x) so that x) dx 1 First find the eigenvalues and orthonormal eigenfunctions for n 1, i.e., An, >,(x). For n 0 there may or may not be an eigenpair. Give all these as a comma separated list....
(1 point) Determine the values of (eigenvalues) for which the boundary-value problem g” + y = 0, 0 < x < 4 y(0) = 0, y' (4) = 0 has a non-trivial solution. An = a , n=1,2,3,... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue in are Yn = Cn* sin(n*pi/2*x) where On is an arbitrary constant.
(1 point) Determine the values of a (eigenvalues) for which the boundary-value problem y + y = 0, 0 < x < 8 y(0) = 0, y'(8) = 0 has a non-trivial solution. = an ((2n-1)^2pi^2)/256 ,n= 1, 2, 3, ... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue an are Yn = Cn* sin ((2n-1) pi n/16) where Cn is an arbitrary cons
4. Consider the following initial value problem of the 1D wave equation with mixed boundary condition IC: u(z, t = 0) = g(x), ut(z, t = 0) = h(z), BC: u(0, t)0, u(l,t) 0, t>0 0 < x < 1, (a)Use the energy method to show that there is at most one solution for the initial-boundary value problem. (b)Suppose u(x,t)-X()T(t) is a seperable solution. Show that X and T satisfy for some λ E R. Find all the eigenvalues An...
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...
ZILLDIFFEQMODAP11 5.2.013. Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + λy = 0, y'(0)= 0, y'(π) = 0
Find the eigenvalues in and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + y = 0, y(0) = 0, y(t) = 0 in = 1, 2, 3, ... în=0 Yn(x) = cos(nx) , n = 1, 2, 3, ... Need Help? Read It Talk to a Tutor
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
Problem #8: Find the eigenfunctions for the following boundary value problem In the eigenfunction take the arbitrary constant (either ci or c2) from the general solution to be 1 Enter your answer as a symbolic function of x,n, as in these examples Do not include 'y-'in your answer. Problem #8 Problem #8: Find the eigenfunctions for the following boundary value problem In the eigenfunction take the arbitrary constant (either ci or c2) from the general solution to be 1 Enter...