Initial data identification in advection–diffusion processes via a reversed fixed-point iteration method

In the present study, a novel method called the reversed fixed-point iteration method (RFPIM) is applied to obtain numerical responses of the advection–diffusion mechanisms. Heretofore, the RFPIM has been employed to find out unstable equilibria of nonlinear mappings defined on Banach spaces. The current paper implements the method to recover the initial data from the final data. The method has been tested under measurements including different levels of noise such as 5%, 10%, 30%, 50%, and 100% in the final time data, and the results indicate that the present technique could be regarded as a powerful tool in handling such inverse problems.