Abstract
The heat equation is a parabolic partial differential equation. This equation considers the variables of time and space to obtain a solution. This study attempts to solve one-dimensional heat equations with a numerical solution approach. The methods used are the Spectral method and the Crank-Nicolson method. The boundary conditions taken for the solution are Dirichlet boundary conditions. To check the reliability of numerical simulation results, the heat equation taken is an equation that has an analytic solution. Maximum errors are needed to compare these two methods. The results are displayed in a table and 3D plots. Numerical simulations show that the Spectral method is quite accurate, but spectral requires more time for simulation. In contrast, the Crank-Nicolson method is more efficient in time for numerical simulations. However, the Crank-Nicolson method is less accurate.
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