Dr. Thomas RannerIBTISAM KHALAF ALSHAMMARI2022-06-062020-11-162022-06-0683696https://drepo.sdl.edu.sa/handle/20.500.14154/67667This thesis reports a variety of linear matrix methods for solving Sylvester Matrix that results from two-dimensional Heat Equation, and demonstrates the advantage of the structure of the problem. Such these linear matrix methods have a significant role in solving this matrix system. Moreover, these methods figure out the best performance and accurate results by observing the algorithm's behavior.53enThesis