Embodiments relate to a 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. A solver stores a plurality of nodes of the domain corresponding to a first time-step, and processes the nodes over a plurality of time-steps using a systolic array comprising hardware for solving the particular type of the differential equation. The systolic array processes each node to generate a node for a subsequent time-step using a sub-array comprising a plurality of branches, each branch comprising a respective set of arithmetic units arranged in accordance with a corresponding term of the discretized form of the differential equation, and an aggregator configured to aggregate the corresponding terms from each branch to generate node data for the subsequent time-step.