Theoretical Numerical Analysis pp 342-404 | Cite as

# Numerical Solution of Fredholm Integral Equations of the Second Kind

Chapter

## Abstract

Linear integral equations of the second kind, were introduced in Chapter 2, and we note that they occur in a wide variety of physical applications. An important class of such equations are the

$$ \lambda u\left( x \right) - \int_D {k\left( {x,\,y} \right){\kern 1pt} u\left( y \right)dy = f\left( x \right)} ,\;x \in D $$

(11.0.1)

*boundary integral equations*, about which more is said in Chapter 12. In the integral of 11.0.1,*D*is a*closed*, and often bounded, integration region. The integral operator is often a compact operator on*C(D*) or*L*^{2}(*D*), although not always. For the case that the integral operator is compact, a general solvability theory is given in Subsection 2.8.4 of Chapter 2. A more general introduction to the theory of such equations is given in Kress [100].## Keywords

Integral Equation Integral Operator Projection Method Node Point Collocation Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag New York, Inc. 2001