Abstract
<jats:p>Ordinary differential equations (ODEs) are essential for modeling and governing physical phenomena and engineering systems across a wide range of scientific and engineering disciplines. Conventional photonic ODE solving systems exhibit a limited coefficient tunability, where the ODE coefficients are constrained by the device architecture. Here, an order- and coefficient-tunable microwave photonic (MWP) ODE solver based on an integrated microcomb source is demonstrated. A transversal filter structure is employed to directly synthesize the desired transfer function through convolution operations, enabling independently tuned ODE coefficients. We experimentally demonstrated simplified first-order, general first-order, and second-order MWP ODE solvers with different coefficients. For the input Gaussian pulse with a pulse width of ~0.1 ns, the measured output waveforms of the ODE solvers agree well with the calculated results, confirming the effectiveness of our approach. A highly reconfigurable MWP ODE solver with high processing accuracy has been achieved by using our approach, which offers a solution for applications in modern control systems, thermal diffusion, and biochemical reactions modelling.</jats:p>