Richard Kowar,
"Parameter Estimation in a Hyperbolic Partial Differential Equation with a Focused Source as Initial Value"
, in ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Seite(n) 113-116, 1999, R. Kowar, Parameter Estimation in a Hyperbolic Partial Differential Equation
with a Focused Source as Initial Value, Technical Report 3/1999, Industrial Mathematics Institute, University of Linz
Original Titel:
Parameter Estimation in a Hyperbolic Partial Differential Equation with a Focused Source as Initial Value
Sprache des Titels:
Englisch
Englische Kurzfassung:
We study the problem of recovering the continuously
varying wave speed in the one-dimensional wave equation
with a focused source as initial data. In this paper this inverse problem is transformed into a parameter estimation problem, which can be solved efficiently. The wave speed can be recalculated by solving an ordinary
differential equation of second order where the parameter of the transformed inverse problem enters as a coefficient. We present a regularized finite difference scheme inversion for the stable recovery of the solution of the transformed parameter estimation problem, which combined with the solution of the ordinary differential equation, gives an estimation for the sound speed.
Journal:
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik
Seitenreferenz:
113-116
Erscheinungsjahr:
1999
Notiz zum Zitat:
R. Kowar, Parameter Estimation in a Hyperbolic Partial Differential Equation
with a Focused Source as Initial Value, Technical Report 3/1999, Industrial Mathematics Institute, University of Linz