NUMERICAL AND ANALYTICAL SOLUTIONS OF VOLTERRAS POPULATION-MODEL

To illustrate various mathematical methods which may be used to solve problems of engineering, mathematical physics, and mathematical biolog y, Volterra's model for population growth of a species in a closed sys tem is solved using several methods familiar to junior-or senior-level students in applied mathematics. Volterra's model is a first-order in tegro-ordinary differential equation where the integral term represent s the effect of toxin accumulation on the species. The solution method s used are (i) numerical methods for solving a first-order initial val ue problem supplemented with numerical integration, (ii) numerical met hods for solving a coupled system of two first-order initial value pro blems, and (iii) phase-plane analysis. A singular perturbation solutio n previously presented is also outlined. While conclusions drawn using the four methods are correlated, the student may analyze and solve th e problem using any of the methods independently of the others.