A fitted numerical method for a system of partial delay differential equations

AbstractWe consider a system of two coupled partial delay differential equations (PDDEs) describing the dynamics of two cooperative species. The original system is reduced to a system of ordinary delay differential equations (DDEs) obtained by applying the method of lines. Then we construct a fitted operator finite difference method (FOFDM) to solve this resulting system. The model considered in this paper is very sensitive to small changes in the parameters associated in with the model. Depending on the values of these parameters, the solution can be stable, periodic and/or aperiodic. Such behavior of the solution is exploited via the proposed FOFDM. This FOFDM is analyzed for convergence and it is seen that this method is unconditionally stable and has the accuracy of O(k+h2), where k and h denote time and space step-sizes, respectively. Some numerical results confirming theoretical observations are also presented. These results are comparable with those obtained in the literature

Information Measures and some Distribution Approximations.

The Fisher and Kullback- Liebler information measures were calculated from the approximation of a binomial distribution by both the Poisson and the normal distributions and are applied to the approximation of a Poisson distribution by a normal distribution. In this paper the concept of relative loss in information due to approximating the distribution of a random variable by that of another distribution of is introduced, and this concept is used to determine the value of the sample size for which the relative loss in information measure is less than a given level