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.