Numerical Procedures For The Determination Of An Unknown Coefficient In Semilinear Parabolic Differential-Equations
Abbreviated Journal Title
INVERSE PROBLEM; PARAMETER; Mathematics, Applied; Physics, Mathematical
We consider a finite difference approximation to an inverse problem of determining an unknown source parameter p(t) which is a coefficient of the solution u in a linear parabolic equation subject to the specification of the solution u at an internal point along with the usual initial boundary conditions. The backward Euler scheme is studied and its convergence is proved via an application of the discrete maximum principle for a transformed problem. Error estimates for u and p involve numerical differentiation of the approximation to the transformed problem. Some experimental numerical results using the newly proposed numerical procedure are discussed.
"Numerical Procedures For The Determination Of An Unknown Coefficient In Semilinear Parabolic Differential-Equations" (1994). Faculty Bibliography 1990s. 999.