Picard-lindel{\"o}f iterations and multiple shooting method for parameter estimation

In this article, we modify the Picard-Lindelöf iteration scheme in order to show an iteration algorithm for parameter estimation of ordinary differential equations.The proposed algorithm inherited the advantages exhibited in the classical algorithms and, moreover, the parameters can be transformed to a form that are convenient and suitable for computation.In the end, a numerical example has also been discused to highlight the results.