EXACT AND NONSTANDARD FINITE DIFFERENCE SCHEMES FOR A MODIFIED LAW OF COOLING
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.
CAU Department of Mathematical Sciences, Department of Physics
Dula, William and Mickens, Ronald E.
"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