On one-dimensional fox-rabies dynamics of advection type

Abstract

A one-dimensional model of fox-rabies of two nonlinear partial differential equations of hyperbolic type is studied. Finite difference techniques are applied to compute the numerical solutions of the initial/boundary value problem. The convergence of the resulting schemes, which have a second order accuracy in space and time, is investigated. The method is tested for different values of advection rate; numerical and graphical results showed that the method is consistent with the dynamic behaviour of fox-rabies.

Keywords:

• hyperbolic type
• initial/boundary value problem
• finite-difference method
• fox-rabies
• advection model
• truncation errors

2000 AMS Mathematics Subject Classifications :

• 35B35
• 35L45
• 35L50

Acknowledgements

This work has been supported by College of Science Research Center, project No. (Math/2008/52), King Saud University.

Notes

Note that the expressions S _t and S _xx , etc., will be used to represent and etc.