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Eigenfunction Expansion

  • Yuri A. Melnikov

Abstract

Having departed for a while from the main focus of the book in the previous chapter, where the emphasis was on ordinary differential equations, we are going to return in the present chapter to partial differential equations. The reader will be provided with a comprehensive review of another approach that has been traditionally employed for the construction of Green’s functions for partial differential equations. The method of eigenfunction expansion will be used, representing one of the most productive and recommended methods in the field.

Keywords

Dirichlet Problem Conformal Mapping Laplace Equation Summation Formula Eigenfunction Expansion 
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.

References

  1. 5.
    V.I. Smirnov, A Course of Higher Mathematics, Vols. 1 and 4, Pergamon, Oxford, 1964 Google Scholar
  2. 6.
    M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965 Google Scholar
  3. 9.
    I.S. Gradstein and I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1971 Google Scholar
  4. 12.
    I.M. Dolgova and Yu.A. Melnikov, Construction of Green’s functions and matrices for equations and systems of elliptic type, J. Appl. Math. Mech., 42 (1978), pp. 740–746. Translation from Russian PMM MathSciNetMATHCrossRefGoogle Scholar
  5. 15.
    R. Haberman, Elementary Applied Partial Differential Equations, Prentice-Hall, New Jersey, 1998 MATHGoogle Scholar
  6. 18.
    M.A. Pinsky, Partial Differential Equations and Boundary-Value Problems with Applications, McGraw-Hill, Boston, 1998 Google Scholar
  7. 25.
    Yu.A. Melnikov and M.Yu. Melnikov, Computability of series representations of Green’s functions in a rectangle, Eng. Anal. Bound. Elem., 30 (2006), pp. 774–780 MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematical Sciences Computational Sciences ProgramMiddle Tennessee State UniversityMurfreesboroUSA

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