A bounded numerical method for approximating a hyperbolic and convective generalization of Fisher’s model with nonlinear damping

We introduce a numerical method for approximating positive and bounded solutions of a time-delayed partial differential equation which generalizes Fisher’s equation from population dynamics. The derivations of the properties of preservation of the positivity and the boundedness of approximations hinge on the fact that, under suitable constraints on the model coefficients and the computational parameters, the method may be represented in vector form using a multiplicative MM-matrix. Our simulations establish that the method proposed in this work conditionally preserves the positivity and the boundedness of the solutions when the lag constant is relatively small. A good agreement between known, exact solutions and the corresponding numerical simulations is recorded in the computational results.