**Numerical Simulations of Some Real-Life Problems Governed by ODEs**

N. H. Sweilam and T. A. Assiri

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63958

## **Abstract**

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In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. These models are the variable-order fractional Hodgkin–Huxley model of neuronal excitation (VOFHHM) and other models with the variable-order fractional (VOF) time delay, such as the 4 year life cycle of a population of lemmings model, the enzyme kinetics with an inhibi‐ tor molecule model, and the Chen system model. A class of numerical methods is used to study the above-mentioned models such as non-standard finite difference (NSFD) and Adams-Bashforth-Moulton (ABM) methods. Numerical test examples are presented.

**Keywords:** Ordinary differential equations, Variable and fractional order real-life mathematical models, Adams-Bashforth-Moulton method, Non-standard finite differ‐ ence method, Error analysis in numerical computations
