Central difference method of a nonstandard inverse heat conduction problem for determining surface heat flux from interior observations (Q2489479)

The authors consider the following nonstandard inverse heat conduction problem in a quarter plane: \[ u_t+u_x=u_{xx} \;x>0,\;t>0, \quad u(x,0)=0, \;x\geq 0, \quad u(1,t)=g(t)\;g(t) \geq 0, \] \(u(x,t)| _{x \to \infty}\) bounded. The author deals with this problem for determining the heat flux distribution by a central difference schemes in time which itself has a regularization effect. The convergence of the surface location \(x=0\), and an error estimate are obtained. A numerical experiment shows that the method works effectively.