A new monotonically stable discrete model for the solution of differential equations emanating from the evaporating raindrop

Abstract

Most of the models of the dynamics of evaporating raindrop have been created using Ordinary Differential Equations. Some models assumed that evaporation is affected by air resistance that is negligible and proportional to the velocity of transition others assumed that the air resistance is significant and proportional to the square of the velocity. Because of the significant differences in the basic assumption used by various modelers, the solution of the resulting equations produced differed values There are yet no work to confirm these dependencies. In this work we obtain a class of hybrid finite difference schemes that can be used to obtain a reliable approximate solution to some of these differential equation models. The schemes were found to possess the same monotonic properties as the analytic solution.