(144b) Inertial Lag and Bessel Composite Function of the Third Order and First Kind Solution to the Dissolving Pill Problem

The finite speed damped wave diffusion and relaxation equation was used to model the transient concentration profile when a pill is dissolving in circular coordinates in all three dimensions. Three regimes of solution was derived using the method of relativistic transformation of coordinates. The damping term was removed from the hyperbolic PDE. The resulting equation was transformed to a Bessel differential equation using a transformation that is symmetrical in space and time. A exterior point in the medium is considered and the inertial time associated with the ballistic accumualtion term was calculated. The second regime was given by a Bessel composite function of the third order among other terms. The third regime for large times, t > X, was given by the modified Bessel composite function of the first kind and third order among other terms. For a given time instant the radius beyond which there was no penetration of mass was calculated. The first zero of the Bessel function of the third order was computed using the first 16 terms of the series expansion of the Bessel function using a Pentium IV prescott microprocessor.