Boundary Conditions at Infinity

  • George Adomian
Part of the Fundamental Theories of Physics book series (FTPH, volume 60)


Solutions of problems with boundary conditions involving a limit at infinity can be difficult. To build some intuition, we will begin with a simple example modelled by a linear differential equation. Consider the function u = e−x = Σ m=0 (−x)m/m!. We obviously have u(0) = 1 and u(∞) = 0. By the latter, we clearly mean that . This function satisfies the differential equation d2u/dx2 − u = 0. Letting L denote d2/dx2, we have Lu−u = 0 which is in our standard format Lu + Ru = 0 with R =− 1. With L1 defined as a two-fold indefinite integration operator, we have L−1Lu = L−1u so that u = C0 + C1 x + L−1u. (Since we are dealing with a linear ordinary differential equation, double decomposition is unnecessary.)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Suggested Reading

  1. 1.
    R. E. Meyer, Introduction to Mathematical Fluid Dynamics, Wiley-Interscience (1971).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • George Adomian
    • 1
  1. 1.General Analytics CorporationAthensUSA

Personalised recommendations