Abstract. In this paper we present a new method for solving systems of ordinary nonlinear differential equations with initial conditions. The method is based on the transformation of the problem to an optimal control problem. We then solve it with a technique based on the use of an integral form of the Euler equation combined with the shooting method and the cyclic coordinate descent method. Our method substantially improves a previous approach that uses iterative dynamic programming to solve the associated optimal control problem. We consider the error functional instead of the classical global error, the error functional obtained by our method being lower than that obtained by classical methods. The method presented in this paper allows us to solve a wide range of nth order ordinary nonlinear differential equations with initial conditions.

The information on the costs, benefits and opportunities is an essential tool for the study of real options in firms that make large investments.We study investment decisions regarding disruptive economies. The real options logic is unsuitable for single-investment events, which are becoming frequent in this type of economies. We propose a strategy for a firm seeking to invest in the very best technology among a sequence of opportunities. If the choice is not the best, the invested capital will be lost. The yield will depend on whether the chosen option is the best and on the investment. Our analysis shows that the optimal strategy for the investing firm is to invest a specific capital in the relatively best option after a threshold which depends on the number of opportunities.