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Unit 10: Green’s Function Method

10.8 Review Questions Notes

1. Find the Green’s function for the one dimensional case given by

d 2
L y 2 y 0
x
dx
with y(0) = y (0), y(1) = y (1)

2 2
2. Find the Green’s function for the boundary value problem 2 0, for
x 2 y 2
r < 0, given that = f(0) for r = a
3. Prove that for the equation

2
z 2 z z
0
x y x y x y
the Green’s function is

(x y ) 2xy ( )(x y ) 2
y
G x , , , .
3
Answers: Self Assessment

x x
1. G , x
x
1 1 2 1
2. G , x x x .
2 4 6

10.9 Further Readings

Books K. Yosida, Lectures in Differential and Integral Equations
Sneddon L.N., Elements of Partial Differential Equations

King A.C, Billingham J. and S.R. Otto, Differential Equations

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