Nonstandard finite difference schemes for differential equations withn+1 distinct fixed-points

We construct nonstandard finite-difference schemes that provide explicit numerical methods for a first-order differential equation with n+1 distinct fixed-points that include 0, where 0 = a 0 < a 1 < a 2 < … < a n and λ is either 1 or − 1. The numerical method is explicit and preserves the critical properties of the differential equation such as the positivity of the solutions, the stability behaviour of all fixed-points, and the monotonicity of solutions within each interval (a i , a i+1) for i = 0, 1,…, n − 1.