Numerics for PDE using EXCEL Anthony Peirce Department of Mathematics University of British Columbia.

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Transcript Numerics for PDE using EXCEL Anthony Peirce Department of Mathematics University of British Columbia.

Numerics for PDE using EXCEL
Anthony Peirce
Department of Mathematics
University of British Columbia
First derivative Approximations
2
Second derivative Approximation
3
1D heat equation
4
Discrete from of 1D heat equation
5
Laplace’s Equation
6
Discretization of Laplace’s Equation
7
Features of point iterative methods
• Consider solving:
•
By iterating the difference equations:
• Using Jacobi iteration:
• Iterate to equilibrium using diffusion equation:
8
The wave equation
9