In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. See also, for example, Green's function and Fredholm theory.

Classification and overview

Various classification methods for integral equations exist. A few standard classifications include distinctions between linear and nonlinear; homogeneous and inhomogeneous; Fredholm and Volterra; first order, second order, and third order; and singular and regular integral equations. or where g(t) vanishes at a finite number of points in (a,b).

Limits of Integration

: An integral equation is called a Fredholm integral equation if both of the limits of integration in all integrals are fixed and constant.)

  • Computational electromagnetics
  • Boundary element method
  • Inverse problems
  • Marchenko equation (inverse scattering transform)
  • Options pricing under jump-diffusion
  • Radiative transfer
  • Renewal theory
  • Viscoelasticity
  • Fluid mechanics

See also

  • Differential equation
  • Integro-differential equation
  • Ruin theory
  • Volterra integral equation

Bibliography

  • Agarwal, Ravi P., and Donal O'Regan. Integral and Integrodifferential Equations: Theory, Method and Applications. Gordon and Breach Science Publishers, 2000.
  • Brunner, Hermann. Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, 2004.
  • Burton, T. A. Volterra Integral and Differential Equations. Elsevier, 2005.
  • Chapter 7 It Mod 02-14-05 – Ira A. Fulton College of Engineering. <nowiki>https://www.et.byu.edu/~vps/ET502WWW/NOTES/CH7m.pdf</nowiki>.
  • Corduneanu, C. Integral Equations and Applications. Cambridge University Press, 2008.
  • Hackbusch, Wolfgang. Integral Equations Theory and Numerical Treatment. Birkhäuser, 1995.
  • Hochstadt, Harry. Integral Equations. Wiley-Interscience/John Wiley & Sons, 1989.
  • "Integral Equation." From Wolfram MathWorld, <nowiki>https://mathworld.wolfram.com/IntegralEquation.html</nowiki>.
  • "Integral Equation." Integral Equation – Encyclopedia of Mathematics, <nowiki>https://encyclopediaofmath.org/wiki/Integral_equation</nowiki>.
  • Jerri, Abdul J. Introduction to Integral Equations with Applications. Sampling Publishing, 2007.
  • Pipkin, A. C. A Course on Integral Equations. Springer-Verlag, 1991.
  • Polëiìanin A. D., and Alexander V. Manzhirov. Handbook of Integral Equations. Chapman & Hall/CRC, 2008.
  • Wazwaz, Abdul-Majid. A First Course in Integral Equations. World Scientific, 2015.

References