EXACT AND NONSTANDARD FINITE DIFFERENCE SCHEMES FOR A MODIFIED LAW OF COOLING

Authors

William Dula, Clark Atlanta University, Atlanta, GA 30314-3773Follow
Ronald E. Mickens, Clark Atlanta University, Atlanta, GA 30314-3773Follow

Abstract

We construct a first-order, nonlinear differential equation to model cooling and heating of a system embedded in a constant temperature environment. The equation generalizes the standard Newton “Law of Cooling” by including an additional nonlinear term which allows for the system to achieve the equilibrium temperature in a finite time. The major goal of this work is to demonstrate that finite difference schemes exist such that they are dynamically consistent with the major features of the experimental data. Both exact and NSFD schemes are formulated and their numerics are investigated, including a detailed comparison of their corresponding numerical solutions.

Acknowledgements

CAU Department of Mathematical Sciences, Department of Physics

Recommended Citation

Dula, William and Mickens, Ronald E. (2019) "EXACT AND NONSTANDARD FINITE DIFFERENCE SCHEMES FOR A MODIFIED LAW OF COOLING," Georgia Journal of Science, Vol. 77, No. 1, Article 120.
Available at: https://digitalcommons.gaacademy.org/gjs/vol77/iss1/120