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Numerical implementation of the ‘summed progressing wave’ formalism. computation of short‐time and long‐time transients
Author(s) -
Gamby D.,
Lamy R.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150605
Subject(s) - formalism (music) , computation , boundary value problem , mathematics , exponential function , initial value problem , mathematical analysis , attenuation , numerical analysis , operator (biology) , differential equation , algorithm , physics , repressor , transcription factor , optics , visual arts , gene , art , musical , biochemistry , chemistry
A mixed initial‐boundary value problem associated with a hyperbolic integro‐differential system is solved by means of the ‘summed progressing wave’ formalism. Once the numerical problem has been set, the pertaining solution methods are described. A simple approximate solution is also proposed. Attenuation functions are calculated through a novel method using the semi‐group property exhibited by the exponential of an integro‐differential operator. The long‐time solution of the problem at hand can be brought out owing to this procedure.