Meshless collocation procedures for time-dependent inverse heat problems

- Local and global meshless methods are proposed for inverse heat problems.
- Heat source and right boundary condition are accurately recovered without regularization technique.
- Stable and accurate solution has been obtained in the case of local meshless method.
- Superiority of the local method has been established through comparison with the methods reported in the literature.

Inverse heat problems are known to be ill-posed, which make them difficult to be solved numerically. In this paper we use meshless methods based on local and global radial basis functions for numerical solution of one- and two-dimensional inverse heat problems. In one-dimensional case, the unknown heat source and the right boundary condition are recovered, while in two-dimensional case, only the unknown heat source is recovered. Comparison of the global and the local meshless numerical schemes based on MQ radial basis function is performed for one- and two-dimensional cases. Several test problems related to inverse heat parabolic PDEs are numerically solved to verify accuracy and efficiency of the local meshless method. Without application of any regularization technique, accurate and stable solution has been obtained in the case of local meshless method for the input data, which is contaminated with a comparatively large level of noise.