A Finite Difference–Hybrid Block Framework for Efficient Solution of Fokker-Planck Problems

We present a new numerical method to solve linear and non-linear Fokker-Planck equations‎. ‎Our technique is based on a combination of finite differences and block hybrid methods‎. ‎First‎, ‎we discretize the Fokker-Planck equation in space through central finite differences, which yields a system of ordinary differential equations‎. ‎Then‎, ‎we employ a one-step hybrid block method with three optimized points to solve the resulting nonlinear system of ordinary differential equations‎. ‎The fundamental properties of the proposed block hybrid method have been investigated‎ ‎in order to address its convergence‎. ‎Numerical results validate the effectiveness of our proposed technique‎.