Advertisement

Numerical Solution of Fredholm Integral Equations of the Second Kind

  • Kendall Atkinson
  • Weimin Han
Part of the Texts in Applied Mathematics book series (TAM, volume 39)

Abstract

Linear integral equations of the second kind,
$$ \lambda u\left( x \right) - \int_D {k\left( {x,\,y} \right){\kern 1pt} u\left( y \right)dy = f\left( x \right)} ,\;x \in D $$
(11.0.1)
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 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 L2(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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Kendall Atkinson
    • 1
  • Weimin Han
    • 2
    • 3
  1. 1.Department of Mathematics, Department of Computer ScienceUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA
  3. 3.Department of MathematicsZhejiang UniversityHangzhouPeople’s Republic of China

Personalised recommendations