An Alternative Computational Approach for the Simulation of Autonomous Dynamical Differential Equations With One, Two and Three Fixed Points

Autonomous Dynamical Differential Equations (ADDEs) with one, two and three fixed points have been found to be applicable in various fields of human endeavor. There is therefore need to find approximate solutions to such differential equations since some of them do not have solutions in closed form. In view of this, we are motivated to develop an alternative computational approach called the Non-Standard Finite Difference Method (NSFDM) for the simulation of such problems. In developing this alternative computational approach, three major steps were adopted. These include the reconstruction of the numerator function, the reconstruction of the denominator function and the nonlocal representation of nonlinear terms that may occur in the ADDE. The research went further to analyze the basic properties of the NSFDM which include positivity of solutions, elementary stability, dynamical consistence, monotone dependence on initial value and monotonicity of solutions. Finally the ADDEs with one, two and three fixed-points were simulated using the new approach in order to test its computational reliability.