Page 485 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 32.5 Review Question

Show that for the unsymmetric Kernel

x
K ( , ) v 2 sin(vx ) sin[(v 1) ]
t
t
v 1
defined on the domain 0 x 2 , 0 t 2 has the iterated Kernel given by
2
1
2
2
t
t
K ( , ) n 1 [v 2 (v 1) (v 2) ...(v n 1) ] sin xv sin[(n v ) ]
x
n
v 1
sin
[Hint: Integrate term-by-term and use the relation lim . u ]
0
Answer: Self Assessment
2
3
1. y(x) = x + xc x c
1 2
(120 )
where C 1 ,
(600 80 5 2 )
2
4 5C 1 (1 /3)
C = .
2 5
32.6 Further Readings

Books Tricomi, F.G., Integral Equations

Yosida, K., Lectures in Differential and Integral Equations

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