A numerical method for free boundary problems for the equation uxx−q(x)u=ut is proposed. The method is based on recent results from transmutation operators theory allowing one to construct efficiently a complete system of solutions for the above equation, generalizing the system of heat polynomials. The corresponding implementation algorithm is presented.

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This paper uses an analytical framework to examine a firm’s investment and switching strategy under uncertainty. The context is the possibility to launch and operate two distinct projects, one at a time, with exposure to a stochastic exogenous price. We allow for multiple switches between the two projects, along with abandonment options from each. These possibilities fundamentally influence the operational strategy. We show that under some conditions, a dichotomous waiting region may arise at the investment stage. In this case we have an inaction region, for a range of prices in a certain bounded interval, where the firm does not invest and waits to have more information about the price evolution. This region vanishes for a high level of uncertainty. Additionally, the firm may operate with a negative instantaneous profit. We prove that investment in this region is never optimal. Numerical examples enable comparative statics, while extension to allow for time-to-build is included.