Wavelet Methods for Optimal Control Problems in Pharmaceutical Research
Optimal control problems and reaction-diffusion systems have many applications in pharmaceutical research. For instance, the enzymatics collagen matrix degradation and the principal process governing drug transport inside a solid tumor could both be described by reaction-diffusion systems. Solving these systems using effective numerical algorithms will benefit drug product design, drug delivery and cancer treatment. Since the traditional numerical solutions to these systems require large memory and long computational times, we will consider wavelet methods which allow us to combine high order accuracy, efficient preconditioning, and adaptive approximations. We expect the wavelet methods to show the superb performance on solving the reaction-diffusion equations. To further improve the numerical performance of the wavelet methods, we will implement multilevel techniques on adaptive grids.