Highlights
In Part A you will obtain a steady solution to the heat equation for this problem using a second order accurate finite difference scheme and an iterative solver. Your goal is to obtain the solutions (T(x, y)) on a range of mesh sizes and use these solutions to estimate the exact value of temperature at location (x = 0.5 m, y = 0.25 m ).
In Part B you will obtain a transient solution to the heat equation for this problem using a first order implicit finite difference discretisation in time. The goal is to report the temperature at location (x = 0.5 , y = 0.25) at time t = 1 s using a number of grid sizes and time steps sizes and estimate the exact solution.
You will present your results for each part in a short report. In this report you must briefly explain your method, the discrete equations solved, how boundary conditions were applied, explain what simulations were performed and how you determined your solution is accurate. Details for each section are given in the following pages.
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