A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease

[EN]In this paper, a nonstandard explicit discretization strategy is considered to construct a new nonstandard finite difference scheme for solving a mathematical model of the influenza disease. The new proposed scheme has some interesting properties such as high accuracy and ease of implementation, as well as some preserving properties of the exact theoretical solution of the SIRC system, like positivity and elementary stability. These characteristics make it suitable for solving efficiently the propose model. We provide some numerical comparisons to illustrate our results

An efficient optimized adaptive step-size hybrid block method for integrating w′′=f(t,w,w′) directly.

[EN]This article addresses the development and analysis of an efficient optimized hybrid block method for integrating general second order initial value problems (IVPs) of ordinary differential equations (ODEs). The construction of the method is based on a combination of two methodologies, namely hybrid and block that result in an efficient implicit numerical integrator. Further, an improved strategy is obtained considering its adaptive step-size formulation. Some numerical experiments have been carried out on solving some well-known problems existing in the literature with fixed and adaptive step-size implementation of the new scheme. Numerical data reveals that the new scheme is a good alternative to existing solvers with comparable properties