Bioinformatics in its interdisciplinary aspects comprises sciences of computers, medicine, biology, mathematics, and statistics. In essence, Bioinformatics uses computers to find causes of diseases and medical solutions. This dissertation addresses all of these sciences to solve one of the most important problems in system biology: solving large systems of ordinary differential equations (ODEs) describing how genetic networks behave using Markov Chain Monte-Carlo (MCMC) and parallel algorithms on General Purpose Graphical Processing Units (GPGPU). We used in this research Neurospora crassa, whish is a model organism that is widely explored and studied, due to its simplicity and its relatedness to the human beings. We predicted and understood the dynamics and the products of all of 2,418 genes that are believed to be under the control of the biological clock in Neurospora crassa. A genetic network that explains mechanistically how the biological clock functions in the filamentous fungus Neurospora crassa has been built and validated against over 31,000 data points from microarray experiments by harnessing the power of the GPGPU and exploiting the hierarchical structure of that genetic network. Various mathematical models, statistical models, and numerical algorithms, such as Galerkins method, in conjunction with Finite Element Method (FEM) piecewise hat functions, Adaptive Runge Kutta method (ARK), and Gauss-Legendre quadrature method are proposed and used on the GPU to accomplish the purpose of this thesis.