arXiv subjects

Isom H. Herron

Publications and source records attributed to Isom H. Herron.

2 recordsLinked to original sources

arXiv2020

Dynamically Consistent Approximate Rational Solutions to the Thomas-Fermi Equation

We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the predicted numerical values of the two approximate solutions, we compare these values with an accurate numerical solution obtained using a fourth-order Runge-Kutta method. We also present several new integral relations satisfied by the bounded solutions of the TF equation

math.CA↗

arXiv2020

A note on exponential-type solutions for the linear, delayed heat partial differential equation

We construct a class of exponential type solutions for the linear, delayed heat equation. These representations may be used to provide a priori ansatzes for certain boundary and/or initial-value problems arising in heat transfer. Several of the important mathematical properties of the representations are examined, including a discussion of the dependence on the delay parameter.

math.AP↗