Construct the Green’s function for the two-point boundary-
value problem
y′′ (x) + ω2y = f (x) ,
y (a) = y (b) = 0.
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Find the Green’s function ?(?, ?) to solve the boundary value problem: ?" = -12 - ?; ?(0) = 0, ?(2) = 0 3. Find the Green's function G(x, t) to solve the boundary value problem: y" = –12 – y; y(0) = 0, y(2) = 0
3. Green's function for a stretched string. Integrate twice to find the solution of the two-point boundary value problem d2y dr.2=f(x), 0<エ<1, y(0) = y(1)=0 in the form 0 Verify that if you differentiate twice under the integral sign and use the jump conditions at ξ you recover the original problem. 3. Green's function for a stretched string. Integrate twice to find the solution of the two-point boundary value problem d2y dr.2=f(x), 0
Consider these two boundary-value problems: Show that if x is a solution of boundary-value problem,... clear steps and brief explanation please 7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution of boundary-value problem ii, then the function y(t) - x((t- a)/h) solves boundary-value problem i, where h b- a. 7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution...
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.) Problem 11. 12 marks] Consider the following two-point...
2. Two-point boundary value problem with Dirichlet condition. Consider the two-point boundary value problem у" = х-уз, у(0) = 0, y(1) = 0. Approximate y'" by (yn-1-2yn ynt1)/Az2 and write the corresponding discretization for this BVP. Take N 4; write the nonlinear system of equations F(y) 0 for the unknowns yi, уг, уз, y4-What is the Jacobian for the problem? Once you have the Jacobian, how do you perform one Newton iteration to solve F(y)-0? 2. Two-point boundary value problem...
This is PDE problem. Please show all steps in detail with neat handwriting. Problem . Consider the function a) Find the full Fourier Series of F(x) a(0, y, t) = u(a, y, t) 0 u(z, 0, t ) = u(z, b, l) = 0 u(z,y,0) = f(z,y), u(x, y,0)-g(x,y), 0<y< b,t0 a) b) Solve the initial-boundary value problem for 2D wave equation. What is the physical interpretation of these boundary conditions
Prove that the following two-point boundary-value problem has a UNIQUE solution. Thank you Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a 7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
#8 i meant to post #4 (8) Find the function whose Fourier transform is f(k)- (9) Find the solution to the heat equation on the real line have the initial (b) Use your Green's function to find the solution when f(x) 1. function to find the solution when f(x)I. (4) Use the Method of Images to construct the Green's function for 2y a2 that is subject to homogeneous Dirichlet boundary conditions. (b) Use your Green's function to solve the boundary...
the below is the previous question solution: 1. Recall the following boundary-value problem on the interval [0, 1] from Homework 2: f" =-Xf, f'(1) =-f(1). f(0) = 0, Show that if (Anh) and to this boundary-value problem, λι, λ2 〉 0, λιメÂn then fi and f2 are orthogonal with respect to the standard inner product (.9)J( gr)dr. (You may use the solution posted on the course website, or work directly from the equation and boundary conditions above.) (λ2'J2) are two...