Hidekazu Yoshioka

A Stochastic Impulse Control Model for Population Management of Fish-Eating Bird Phalacrocorax Carbo and Its Numerical Computation

Feeding damage from a fish-eating bird Phalacrocorax carbo to a fish Plecoglossus altivelis is severe in Japan. A stochastic impulse control model is introduced for finding the cost-effective and ecologically conscious population management policy of the bird. The optimal management policy is of a threshold type; if the population reaches an upper threshold, then taking a countermeasure to immediately reduce the bird to a lower threshold. This optimal policy is found through solving a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose a numerical method for HJBQVIs based on a policy iteration approach. Its accuracy on numerical solutions and the associated free boundaries for the management thresholds of the population, is investigated against an exact solution. The computational results indicate that the proposed numerical scheme can successfully solve the HJBQVI with the first-order computational accuracy. In addition, it is shown that the scheme captures the free boundaries subject to errors smaller than element lengths.

Wise-Use of Sediment for River Restoration: Numerical Approach via HJBQVI

A stochastic differential game for cost-effective restoration of river environment based on sediment wise-use, an urgent environmental issue, is formulated. River restoration here means extermination of harmful algae in dam downstream. The algae population has weak tolerance against turbid river water flow, which is why the sediment is focused on in this paper. Finding the optimal strategy of the sediment transport reduces to solving a spatio-temporally 4-D Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJBQVI): a degenerate nonlinear and nonlocal parabolic problem. Solving the HJBQVI is carried out with a specialized finite difference scheme based on an exponentially-fitted discretization with penalization, which generates stable numerical solutions. An algorithm for solving the discretized HJBQVI without resorting to the conventional iterative matrix inversion methods is then presented. The HJBQVI is applied to a real problem in a Japanese river where local fishery cooperatives and local government have been continuing to debate the way of using some stored sediment in a diversion channel for flood mitigation. Our computational results indicate when and how much amount of the sediment should be applied to the river restoration, which can be useful for their decision-making.