This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via root mean squares error (RMSE). We found that the numerical results are accurate and stable.
Load balancing in computer networks is one of the most subjects that has got researcher's attention in the last decade. Load balancing will lead to reduce processing time and memory usage that are the most two concerns of the network companies in now days, and they are the most two factors that determine if the approach is worthy applicable or not. There are two kinds of load balancing, distributing jobs among other servers before processing starts and stays at that server to the end of the process is called static load balancing, and moving jobs during processing is called dynamic load balancing. In this research, two algorithms are designed and implemented, the History Usage (HU) algorithm that statically balances the load of a Loaded
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