Due to the end of Moore’s law and Dennard scaling, we are entering a new era of processors. Computing systems are increasingly facing power and performance challenges due to both device- and circuit-related challenges with resistive and capacitive charging. Non-von Neumann architectures are needed to support future computations through innovative post-Moore’s law architectures. To enable these emerging architectures with high-performance and at ultra-low power, both parallel computation and inter-node communication on-the-chip can be supported using photons. To this end, we introduce ROC, a reconfigurable optical computer that can solve partial differential equations (PDEs). PDE solvers form the basis for many traditional simulation problems in science and engineering that are currently performed on supercomputers. Instead of solving problems iteratively, the proposed engine uses a resistive mesh architecture to solve a PDE in a single iteration (one-shot). Instead of using actual electrical circuits, the physical underlying hardware emulates such structures using a silicon-photonics mesh that splits light into separate pathways, allowing it to add or subtract optical power analogous to programmable resistors. The time to obtain the PDE solution then only depends on the time-of-flight of a photon through the programmed mesh, which can be on the order of 10’s of picoseconds given the millimeter-compact integrated photonic circuit. Numerically validated experimental results show that, over multiple configurations, ROC can achieve several orders of magnitude improvement over state-of-the-art GPUs when speed, power, and size are taken into account. Further, it comes within approximately 90% precision of current numerical solvers. As such, ROC can be a viable reconfigurable, approximate computer with the potential for more precise results when replacing silicon-photonics building blocks with nanoscale photonic lumped-elements.