Title: Solution of the One−Dimensional Monoenergetic Fokker–Planck Equation by Lagrange Interpolation
Abstract: In this work, we formulate a response−matrix solution of the one−dimensional monoenergetic Fokker–Planck equation using Lagrange interpolation for the angular variable. First−and second−derivative Lagrange differentiation matrices evaluated on full−range Legendre abscissae represent the angular differential scattering operator. The representation also produces a discrete ordinates balance equation analogous in structure to the standard Boltzmann discrete ordinates equation, but for a differential angular scattering operator. A hyperbolic response−matrix form then solves the resulting first−order spatial system, replacing the matrix−exponential representation. Numerical results show that the Lagrange interpolation formulation reproduces the previously reported benchmark behavior while providing an independent angular discretization and a canonical hyperbolic response−matrix construction.