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Abstract

It was stated in Chapter 2 that Fredholm integral equations arise in many scientific applications. It was also shown that Fredholm integral equations can be derived from boundary value problems. Erik Ivar Fredholm (1866– 1927) is best remembered for his work on integral equations and spectral theory. Fredholm was a Swedish mathematician who established the theory of integral equations and his 1903 paper in Acta Mathematica played a major role in the establishment of operator theory.

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References

  1. W.V. Lovitt, Linear Integral Equations, Dover, New York, (1950).

    Google Scholar 

  2. G. Adomian, Solving Frontier Problems of Physics, The Decomposition Method, Kluwer, Boston, (1994).

    MATH  Google Scholar 

  3. G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Modelling, 13 (1992) 17–43.

    Article  MathSciNet  Google Scholar 

  4. A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, HEP and Springer, Beijing and Berlin, (2009).

    Google Scholar 

  5. A.M. Wazwaz, A First Course in Integral Equations, World Scientific Singapore, (1997).

    Google Scholar 

  6. A.M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, Appl. Math. Comput., 81 (1997) 199–204.

    Article  MathSciNet  Google Scholar 

  7. L.M. Delves, and J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, London, (1974).

    MATH  Google Scholar 

  8. J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential equations, Yale University Press, New Haven, (1923).

    MATH  Google Scholar 

  9. R. Kress, Linear Integral Equations, Springer, Berlin, (1999).

    Book  MATH  Google Scholar 

  10. J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178 (1999) 257–262.

    Article  MATH  Google Scholar 

  11. D.L. Phillips, A technique for the numerical solution of certain integral equations of the first kind, J. Assoc. Comput. Mach, 9 (1962) 84–96.

    MathSciNet  MATH  Google Scholar 

  12. A.N. Tikhonov, On the solution of incorrectly posed problem and the method of regularization, Soviet Math, 4 (1963) 1035–1038.

    Google Scholar 

  13. R.F. Churchhouse, Handbook of Applicable Mathematics, Wiley, New York, (1981).

    Google Scholar 

  14. Y. Cherruault and V. Seng, The resolution of non-linear integral equations of the first kind using the decomposition method of Adomian, Kybernetes, 26 (1997) 109–206.

    MathSciNet  Google Scholar 

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© 2011 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Wazwaz, AM. (2011). Fredholm Integral Equations. In: Linear and Nonlinear Integral Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21449-3_4

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