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)


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


Integral Equation Integral Operator Projection Method Node Point Collocation Method 
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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

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