Advertisement

Separability of PDE

  • Gianpietro Elvio CossaliEmail author
  • Simona Tonini
Chapter
  • 3 Downloads
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

The analytical modelling of heat and mass transfer phenomena relies on the analytical solutions to partial differential equations, which are used to describe the conservation of mass, chemical species, momentum and energy and their transfer mechanisms, as it will be shown in Part II of this book. Analytical methods for this kind of problems are widely used (see [1]) and among the several available techniques to solve Partial Differential Equations (PDE), separation of variable is generally the most valuable one since it may yield solutions in a form that is easily implementable for routine calculations. Separability of a PDE depends on the chosen coordinate system and this chapter is devoted to analyse conditions and methods for PDE separation.

References

  1. 1.
    Weigand, B.: Analytical Methods for Heat Transfer and Fluid Flow Problems. Springer, Berlin (2004)CrossRefGoogle Scholar
  2. 2.
    Moon, P., Spencer, D.E.: Field Theory Handbook, 2nd edn. Springer, Berlin (1971)CrossRefGoogle Scholar
  3. 3.
    Morse, P.M., Feshback, H.: Methods of Theoretical Physics. McGraw Hill, New York (1953)Google Scholar
  4. 4.
    Moon, P., Spencer, D.E.: Separability conditions for the Laplace and Helmholtz equations. J. Franklin Inst. 253(6), 585–600 (1952)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Moon, P., Spencer, D.E.: Separability in a class of coordinate systems. J. Franklin Inst. 254(3), 227–242 (1952)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Levison, N., Bogert, B., Redheffer, R.M.: Separation of Laplace’s equation. Quart. Appl. Math. 7(3), 241–262 (1949)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Moon, P., Spencer, D.E.: Recent investigation of the separation of Laplace’s equation. Proc. Amer. Math. Soc. 4(2), 302–307 (1953)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Robertson, H.P.: Bemerkung über separierbare systeme in der Wellenmechanik (in German). Math. Ann. 98, 749–752 (1927)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Department of Engineering and Applied SciencesUniversity of BergamoDalmineItaly

Personalised recommendations