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The aim of this work is to use a variety of numerical methods by applying them to the solution of elliptic equations. Elliptic equations are building blocks of partial differential equation. Steady state heat diffusion is characterized by their elliptic nature of governing equations. In this book three different numerical techniques are used to solve steady state heat diffusion equation. Plots showing the results for three methods to solve the equation are shown and the programs written in MATLAB are also shown at the end of the paper. The solution provides the steady state heat diffusion pattern within the rectangular thin plate.