THE DETERMINATION OF MULTIPLE COEFFICIENTS IN A 2ND-ORDER DIFFERENTIAL-EQUATION FROM INPUT SOURCES

Authors
LOWE BD RUNDELL W
Citation
Bd. Lowe et W. Rundell, THE DETERMINATION OF MULTIPLE COEFFICIENTS IN A 2ND-ORDER DIFFERENTIAL-EQUATION FROM INPUT SOURCES, Inverse problems, 9(4), 1993, pp. 469-482
Citations number
10
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics,"Physycs, Mathematical",Mathematics
Journal title
Inverse problems → ACNP
ISSN journal
02665611
Volume
9
Issue
4
Year of publication
1993
Pages
469 - 482
Database
ISI
SICI code
0266-5611(1993)9:4<469:TDOMCI>2.0.ZU;2-0
Abstract
We consider the question of recovering the coefficients a and q from t he equation -(a(x)u'j(x))' + q(x)u(j)(x) = f(j)(x) with boundary condi tions u(j)(0) = u(j)(1) = 0, and where the non-homogeneous source term s {f(j)(x)}j=1 infinity form a basis for L2(0, 1). We will prove that a unique determination is possible from data measurements {a(0)u'j(0), a(1)u'j(1)}j=1 infinity. An algorithm that allows efficient numerical reconstruction of a(x) and q(x) from finite data is given.