Before revision:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
After revision:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to finance), and elliptic. We generically obtain improved convergence rates relative to typical past implementations relying on delta function approximations .