Inverse Estimation of 1-D Heat Problem with Neumann Boundary Condition by Morozov Discrepancy Principle

Abstract

Consider a 1-D backward heat conduction problem with Neumann boundary conditions. We recover u(x, 0) from the measured data u(x, t) means, initial temperature from the measurement of final temperature. In this work basic tools are Tikhonov regularization and Morozov's discrepancy principle. The regularization parameter is computed by the discrepancy principle of Morozov, and a first-kind Fredholm integral equation is used for numerical simulation.