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→Example: 2D diffusion equation: added "second" for central differences and reviewed some of the notation (previously confusing) |
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: <math>{u_{ij}^{n+1/2}-u_{ij}^n\over \Delta t/2} =
{\left(\delta_x^2 u_{ij}^{n+1/2}+\delta_y^2 u_{ij}^{n}\right)\over \Delta x^2}</math>
: <math>{u_{ij}^{n+1}-u_{ij}^{n+1/2}\over \Delta t/2} =
{\left(\delta_x^2 u_{ij}^{n+1/2}+\delta_y^2 u_{ij}^{n+1}\right)\over \Delta y^2}</math>
The system of equations involved is [[symmetric matrix|symmetric]] and tridiagonal (banded with bandwidth 3), and is typically solved using [[tridiagonal matrix algorithm]].
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