The main purpose of this paper is to treat the problem of numerical solutions of Lyapunov matrix equations and nonlinear matrix equations such as the Riccati type which occur in many areas of applications such as in control theory, robotics, mathematical modelling and computer simulation, etc. The main approach is to obtain solutions of such type equations in a more direct manner as in contrast to completely interactive methods. Parallel processing of algorithms is made use of in the computation of solutions of such nonlinear matrix equations associated with nonlinear matrix differential equations arising in the study of nonlinear dynamical control systems.