Embodiments relate to a computing system for solving differential equations. The system is configured to receive problem packages corresponding to problems to be solved, each comprising at least a differential equation and a domain, and to select a solver of a plurality of solvers, based upon availability of each of the plurality of solvers. A dispatch computer selects a solver by monitoring the plurality of solvers, and responsive to a solver becoming available, determines if a received problem package having at least a threshold priority level can be solved by the solver. Otherwise, the dispatch computer generates a plurality of solver scenarios each reflecting a permutation of received problem packages assigned to solvers estimated to become available within a threshold period of time, and assigns the problem packages in accordance with a solver scenario having a highest utilization score.