عارفه مومني

This thesis presents an‎d analysis an efficient numerical method for solving time fractional order partial differential equations of parabolic type, including convection-diffusion, reaction-diffusion, an‎d fractional diffusion equations. The proposed method is based on spectral collocation method using the operational matrices of orthogonalized Bernoulli polynomials. In this method, by approximating the time fractional derivatives present in the equations, the supposed equation is transformed into a system of algebraic equations. Then, by solving this system, the unknown coefficients of the series expansion an‎d finally the numerical solution of the equations are obtained. The convergence of the presented numerical method has been theoretically investigated an‎d proven. To demonstrate the effectiveness, accuracy, an‎d practical application of the proposed method, various numerical examples are presented an‎d the results are compared with methods available in other references. Comparisons show that the method developed in this thesis has higher accuracy an‎d is simpler to impleme nt.

معادله همرفت انتشار كسري وابسته به زمان , معادله واكنش- انتشار كسري , معادله انتشار كسري , چندجمله‌اي‌هاي برنولي متعامد , روش‌ هم‌محلي , همگرايي

Time fractional convection-diffusion , fractional reaction-diffusion , Fractional diffusion equation , Orthogonalized Bernoulli polynomials , Orthogonalized Bernoulli polynomials , Collocation methods , convergence

Momeni

Dr, rashidinia