Green's function

(Also called influence function.) A function that is the known solution of a homogenous differential equation in a specified region and that may be generalized (if the equation is linear) to satisfy given boundary or initial conditions, or a nonhomogeneous differential equation.

It is thus an alternative method to the Fourier transform or Laplace transform, applicable to many of the same problems. The Green's function method takes a fundamental solution and assigns it a weight at each point, say, of the boundary, according to the value of the given boundary condition there; the Fourier method analyzes the entire boundary condition into wave components thus assigning each of these a weight or amplitude. Both methods then obtain the final solution by summation or integration.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.