AbstractWe investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modified kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and effective approximation to the solution of the inverse and ill-posed problem.
Numerical Solution of Ill Posed Problems in Partial Differential Equations.