Special Session 69: Lie Symmetries, Conservation laws and other approaches in solving nonlinear differential equations
Contents
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs).
The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple
illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered.