The determination of multiple coefficients in a second-order differential equation from input sources Academic Article uri icon

abstract

  • The authors consider the question of recovering the coefficients a and q from the equation -(a(x)u'j(x))'+q(x)uj(x)=f j(x) with boundary conditions uj(0)=uj(1)=0, and where the non-homogeneous source terms (fj(x))j=1infinity form a basis for L2(0,1). They prove that a unique determination is possible from data measurements (a(0)u'j(0), a(1)u'j(1))j=1infinity. An algorithm that allows efficient numerical reconstruction of a(x) and q(x) from finite data is given.

author list (cited authors)

  • Lowe, B. D., & Rundell, W.

citation count

  • 5

publication date

  • August 1993