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Show that the BVP, Uxx = f(x), 0≤x≤1 ux (0)=0=ux(1) has a unique solution if and only if f₁₁f(x)dx=0 This says that f is perpendicular to the constant (basis) functions. Find the solution and the Green's function with free boundary conditions, G(x,y)=-2Σ n=1 cos (ntx) cos (nity) n²π²

Show that the BVP, Uxx = f(x), 0≤x≤1 ux (0)=0=ux(1) has a unique solution if and only if f₁₁f(x)dx=0 This says that f is perpendicular to the constant (basis) functions. Find the solution and the Green's function with free boundary conditions, G(x,y)=-2Σ n=1 cos (ntx) cos (nity) n²π²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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correction for the question: the solution is not unique. It is only unique up to a constant.

homework practice, this class is about Fourier series; generalized functions; and numerical methods.

please show clear thanks

7. Show that the BVP, Uxx = f(x), 0≤x≤1 ux (0)=0=ux (1) has a unique solution if and only if [fixar o This says that f is perpendicular to the constant (basis) functions. Find the solution and the Green's function with free boundary conditions, 00 G(x,y) = -2 Σ n=1 cos (ntx) cos (ny) n²π²
Transcribed Image Text:7. Show that the BVP, Uxx = f(x), 0≤x≤1 ux (0)=0=ux (1) has a unique solution if and only if [fixar o This says that f is perpendicular to the constant (basis) functions. Find the solution and the Green's function with free boundary conditions, 00 G(x,y) = -2 Σ n=1 cos (ntx) cos (ny) n²π²
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