Page 466 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Unit 30: Neumann s Series

30.4 Keywords Notes

The C(a, b) is a space of all continuous functions defined on the interval (a, b).
2
The unknown functions y(x) and f(x) are of C(a, b) type while K(x, t) is of C (a, b) C (a, b) type on
the square a x b and a t b.

30.5 Review Question

Solve the Fredholm integral equation of the second kind

1
x
t
y
x
Y ( ) f ( ) x (1 t ) ( )dt
0
when is not an eigenvalue.
Answer: Self Assessment
K C b
x
1. y ( ) f ( ) o o , C 0 f ( )dx
x
x
1 K 0 (b a )] a
1
Expand in powers of to get Neumann Series.
1 K 0 (b ) a
30.6 Further Readings

Books Erwin Kreyzig, Introductory Functional Analysis with Applications
Tricomi, F.G., Integral Equations
Yosida, K., Lectures in Differential and Integral Equations

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