Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

This thesis is a contribution on optimization techniques for some bioinformatics models. These models are, the diffusion model, the cable equation for modeling neuronal dynamics, susceptible - infected - recovered and cross-immune (SIRC) model, and tumor immune model. The diffusion equation and the cable equation are introduced here as fractional order models, the fractional derivative is described in the Caputo{u2019}s sense. A Crank-Nicolson finite difference method for the time fractional parabolic equation on a distributed system using Message Passing Interface (MPI) is investigated. The weighted average finite difference method is used to discretized the cable equation, the resultant large system of equations of both the timefractional parabolic equation and the cable equation is studied using parallel preconditioned conjugate gradient method, with the implementation of cluster computing on it. Also, SIRC model has introduced as a fractional order model and the fractional derivative is described in the Caputo{u2019}s sense. The Chebyshev spectral method is implemented for solving this model. The properties of the Chebyshev polynomials are used to reduce the proposed problem to the solution of a system of algebraic equations which are solved by using dogleg trust region method

Issued also as CD