Chapter 5 delves into the development of multiple algorithms tailored for numerically solving optimal feedback control problems utilizing the dynamic programming viscosity solution (DPVS) approach. The objective is to devise truly effective algorithms capable of proving convergence, with a focus on distributed parameter systems with widespread real-world applications. The chapter presents a direction derivative algorithm, an interpolation algorithm, time difference and time-space approximation schemes, and a local approximation algorithm. Each algorithm is designed to address specific challenges in solving optimal control problems, and the convergence of an upwind finite-difference scheme is rigorously proven. The comprehensive study offers valuable insights into the application and refinement of the DPVS approach for numerical optimal control.