Numerical time perturbation and resummation methods for nonlinear ODE

In this research work, numerical time perturbation methods are applied on nonlinear ODE. Solutions are sought in the form of power series using time as the perturbation parameter. This time integration approach with continuation procedures allows to obtain analytical continuous approximated solutions. Asymptotic Numerical Method and new resummations techniques of divergent series namely Borel–Padé–Laplace and Inverse Factorial series are studied. A comparison with classic integration scheme is presented in order to evaluate the robustness and the effectiveness of these algorithms. Full details are given regarding first- and second-order derivative of resummation techniques.