الفهرس 
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Abstract
This thesis discusses. the optimal reactor operation. Optimal reactor operation can be
achieved by an accurate estimate of the neutron flux, effective multiplication factor and control rod worth. In our work, we develop fast and general algorithms for numerically solving a neutron diffusion equation by a Wavelet Ga1crkin method (WGM) to be used in the reactor different parameter calculations. Our motivation is the neutron diffusiol1 equation. which will be discussed in section. 1.1. We prepare some standard notations and terminology used to solve a partial differential equations using wavelet theory in section 1.2. Then, in section 1.3 we present the solution procedure of the neutron diffusion equation in both static and quasi-static cases. Chapter 2, we make a survey for the previous work. The previous work for solving partial differential equations using wavelet theory in general is presented including the effort of the researchers of the developing. On other hand, the previous effort for solving neutron diffusion equation using a conventional methods and a brief description for the neutronics codes depends on the diffusion equation is also presented. In chapter 3; we demonstrate a complete illustration of the wavelet system design. We first introduce the fundamentals of wavelets and its properties in sections 3.1 and 3.2. In section 3.3 we. start designing the wavelet system that we. use in the solution of the diffusion equation by calculating the scaling coefficients, after that in section 3.4, we obtain the scaling functions that we use finally to calculate the mother wavelet function in sectioi’1 3.5. These procedure to obtain the mother wavelet function is not new, but the technique we used to obtain the scaling coefficients is new and enable us to get a wavelet
. system to higher wavelet order with high accuracy. In Chapter 4, we discus the idea of obtaining the connection coefficients analytically. This analytical solution of the connection coefficients enables us to overcome the unstability of the wavelet derivatives and let us use higher order wavelets for solving the diffusion equations. This technique gives us more accurate solution for the diffusion.