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Explicit and approximate solutions of second‐order evolution differential equations in Hilbert space
Author(s) -
Gavrilyuk Ivan P.,
Makarov Vladimir L.
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199901)15:1<111::aid-num6>3.0.co;2-l
Subject(s) - mathematics , hilbert space , smoothness , constant coefficients , mathematical analysis , hyperbolic partial differential equation , space (punctuation) , constant (computer programming) , partial differential equation , operator (biology) , differential equation , euler's formula , differential operator , first order partial differential equation , computer science , philosophy , linguistics , biochemistry , chemistry , repressor , transcription factor , gene , programming language
The explicit closed‐form solutions for a second‐order differential equation with a constant self‐adjoint positive definite operator coefficient A (the hyperbolic case) and for the abstract Euler–Poisson–Darboux equation in a Hilbert space are presented. On the basis of these representations, we propose approximate solutions and give error estimates. The accuracy of the approximation automatically depends on the smoothness of the initial data. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 111–131, 1999