A numerical method for solving the inverse heat conduction problem without initial value

摘要

We consider the inverse heat conduction problem for the one-dimensional heat equation, where we are requested to determine a boundary value at one end of a spatial interval over a time interval and an initial value by means of Cauchy data at another end. By the existing theory we can prove the uniqueness in determining both a boundary value and an initial value, and our method does not require any initial value. We test our numerical method and show stable numerical reconstruction.