Integral Models Of Physical Systems

  • Natali Hritonenko
  • Yuri Yatsenko
Part of the Applied Optimization book series (APOP, volume 81)


Integral equations represent a more general tool for solving applied engineering problems as compared with differential equations. An integral equation “represents the entire physics of the problem in a very compact form and, in many instances, a more convenient form than the more conventional differential equation” ( Morse and Feshbach, 1953, p.896). Generally speaking, integral equations (IEs) can describe global situations that cannot be modeled by differential equations. On the other hand, all models based on DEs may be converted to IEs. The corresponding applications include many problems of viscoelasticity ( Renardy et al, 1987) and creep theory ( Arutjunian and Kolmanovskii, 1983), superfluidity ( Miller, 1973) and aeroelasticity ( Belotserkovskii et al, 1980), coagulation and meteorology (Galkin and Dubovskii, 1982), electromagnetism ( Bloom, 1981), radiation transfer ( Cergignani, 1975;  Colton and Kress, 1983), radiophysics ( Ramm, 1980), electronic lithography, astronomy, and so on.


Boundary Integral Equation Nonlinear Integral Equation Differential Model Mine Elevator Nonlinear Volterra Integral Equation 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Natali Hritonenko
    • 1
  • Yuri Yatsenko
    • 2
  1. 1.Department of MathematicsPrairie View A&M UniversityPrairie ViewUSA
  2. 2.College of Business and EconomicsHouston Baptist UniversityHoustonUSA

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