please can I ask a bit stupid question? Let say I need to solve an equation in a form $\frac{\partial X}{\partial t}=\sum_k M_k * X_{n-k}$ How can I do the discrete convolution numerically? I will say I will expand X into series (FFT) and then, please? Many thanks

please can I ask a bit stupid question? Let say I need to solve an equation in a form $\frac{\partial X}{\partial t}=\sum_k M_k * X_{n-k}$ How can I do the discrete convolution numerically? I will say I will expand X into series (FFT) and then, please? I have a layer of free surfaces on the top and bottom and from the sides the material can inflow/outflow.. Many thanks